For the cookie base: In a small bowl, beat together egg and vanilla extract until the yolk is broken up and evenly combined; set aside. Combine flour, sugar, salt, and baking powder in the bowl of a food processor fitted with a blade attachment and pulse a few times to aerate and break up any lumps. Add butter and pulse until the mixture looks like sand, about 25 1-second pulses. Add egg mixture and pulse until the dough just forms into a ball, about 25 1-second pulses. Turn dough out onto a clean work surface and form into a circle, then flatten into a disk. Wrap in plastic and refrigerate for at least 1 hour. Heat the oven to 375°F and arrange a rack in the middle. Lightly flour a 14-inch piece of parchment paper and place the chilled dough disk on top. Lightly flour the top of the dough disk and roll out to 1/8 inch thick. (Work quickly; the dough will become difficult to roll as it warms up.) Transfer the dough and parchment paper to a baking sheet, cover with another piece of parchment paper, and freeze for 5 minutes. Peel the parchment paper off the dough and then lightly press it back down onto the surface of the dough (this will prevent the dough from sticking to the parchment as the cookies are cut out). Flip the dough over and remove the other piece of parchment paper. Using a small round cookie cutter about 2 inches in diameter, stamp out as many cookies as possible. Then, using a smaller round cookie cutter about 1 inch in diameter, stamp out the center of each cookie. Reserve the dough centers. Place the cookies 1/4 inch apart on an ungreased baking sheet. (About 28 cookies will fit on 1 sheet.) Bake until the edges are golden brown, about 10 to 12 minutes. Remove to a wire rack to cool completely. While the cookies are baking, gather the scraps of dough and reserved centers, form them into a flattened disk, and wrap in plastic. Place the disk in the freezer for 5 minutes, then repeat the process until all the cookie dough has been used. For the caramel topping: Combine sugar, water, and salt in a small saucepan and bring to a boil over medium heat, stirring once to dissolve the sugar. Continue to boil, swirling the pan occasionally (but not stirring), until the mixture turns a deep amber color, about 15 minutes. Remove from heat, carefully pour in cream and vanilla (the mixture will bubble up and steam), and stir until evenly combined. Transfer to a heatproof bowl; set aside. To temper the chocolate: Prepare an ice water bath by filling a large bowl with 2 inches of cold water and adding 3 to 4 ice cubes; set aside. Bring a medium saucepan filled with 1 to 2 inches of water to a simmer over high heat; once simmering, turn off heat. Place 18 ounces of the chocolate couverture in a dry, heatproof bowl. Set the bowl over the saucepan and stir until the chocolate is completely melted and has reached 118°F. (Make sure the chocolate does not come in contact with water or exceed 120°F. If either happens, start over, as the chocolate will no longer be usable.) Remove the bowl from the saucepan. Add the remaining 6 ounces chocolate and stir until all the chocolate has melted and the temperature has cooled to 80°F. To speed up the cooling process—but only after all of the chocolate has melted—place the bowl over the reserved ice water bath. Return the bowl of chocolate to the saucepan and stir until the chocolate reaches 88°F; immediately remove from heat. Do not remove the thermometer from the bowl; check the temperature periodically to make sure it stays between 87°F and 89°F. (The chocolate must remain in this temperature range while dipping the cookies or it will not set properly.) Keep the saucepan of water over low heat and, when needed, set the bowl of chocolate over it to reheat. To test if the chocolate is properly tempered, spread a thin layer on parchment paper and place it in the refrigerator for 3 minutes to set. If the chocolate hardens smooth and without streaks, it is properly tempered. (If it is not properly tempered, let the melted chocolate harden and start the tempering process over again: Bring the chocolate up to 118°F, then down to 80°F, then up again to 88°F.) To assemble the cookies: Line 2 baking sheets with parchment paper; set aside. Pick up a cookie by the outer edge. Dip only the flat bottom into the chocolate, then scrape the bottom against the edge of the bowl to remove any excess chocolate. Set on one of the prepared baking sheets, chocolate side down, and repeat with the remaining cookies. Let sit at room temperature until completely set, about 10 minutes, or freeze for 5 minutes. (While the chocolate is setting, and during the caramel-dipping process, remember to keep the bowl of melted chocolate in temper at 87°F to 89°F for the final cookie dipping.) Meanwhile, make sure the caramel is the right consistency for dipping; it should be warm to the touch and still pourable like syrup but not so hot that it will burn your fingers. If it’s too stiff, warm it up for 2 to 3 minutes over low heat while stirring. Place the toasted coconut in a medium bowl. When the chocolate on the cookies is set, flip the cookies chocolate side up. Pick up a cookie by the outer edge and dip the top into the caramel, letting any excess drip off and making sure the center hole is free of caramel, then immediately dip the caramel side into the toasted coconut. Set the cookie back on the baking sheet coconut side up and repeat with the remaining cookies. Place about 1 cup of the tempered chocolate in a resealable plastic bag, preferably a strong freezer bag. Cut an 1/8-inch opening in the corner of the bag and drizzle chocolate over the cookies in a zigzag pattern. Let the chocolate and caramel completely set before eating, about 20 minutes. Store in an airtight container at room temperature for 1 week or in the freezer for up to 1 month.