Make the pastry cream Drain the ricotta in a fine sieve set over a small bowl in the refrigerator for at least 4 hours and up to 1 day. Warm the milk in a heavy-duty 3-quart saucepan over medium heat until steaming, 3 to 4 minutes. Meanwhile, whisk the eggs, egg yolks, and 1/2 tsp. salt in a medium bowl. Gradually whisk in the sugar. Whisk in the cornstarch and vanilla until smooth. Slowly whisk a little of the hot milk into the egg mixture to warm it, then whisk the mixture into the pot of milk. Whisk in the butter and cook over medium heat, whisking constantly, until the pastry cream is very thick and registers 165°F on an instant-read thermometer, 2 to 3 minutes. Strain through a fine sieve into a medium bowl. Cover with plastic wrap, pressing it onto the surface of the cream, and refrigerate for at least 2 hours. Purée the ricotta in a food processor until very smooth, about 8 minutes. Stir it into the pastry cream and refrigerate until ready to use or for up to 1 day. Make and fill the pâte à choux puffs Position racks in the upper and lower thirds of the oven and heat the oven to 425°F. Bring 2-1/2 cups of water and the butter, sugar, and 1-1/4 tsp. salt to a boil in a 4-quart saucepan over medium-low heat. When the butter melts, remove from the heat and add the flour. Set the pan over low heat and stir with a wooden spoon until the mixture forms a smooth ball that pulls away from the sides of the pan, about 2 minutes. Transfer the mixture to a stand mixer fitted with the paddle attachment and beat on low speed until cool to the touch. On medium-low speed, beat in the eggs one by one, mixing until each is fully incorporated before adding the next. Let the dough cool for about 10 minutes. Transfer half of the dough to a pastry bag fitted with a 1/2-inch plain tip (Ateco #806). Onto 2 parchment-lined rimmed baking sheets, pipe small, 1-1/2-inch-high mounds (like chocolate kisses) at 2-inch intervals. Smooth the surface of the mounds with a wet finger. Lower the oven temperature to 375°F and bake, rotating the sheets from top to bottom after 10 minutes, until the puffs are evenly golden-brown, 20 to 25 minutes total. Turn off the oven and remove the puffs from the oven. Prick the side of each puff with a paring knife to release the steam. Return the puffs to the turned-off oven with the door ajar to dry them for 3 to 5 minutes. Remove the puffs from the baking sheets and transfer to a rack to cool. Repeat with the remaining dough on freshly lined baking sheets. Assemble the croquembouche Sort the puffs according to size: small, medium, and large. Transfer about half of the pastry cream to a piping bag fitted with a 1/4-inch plain tip (Ateco # 802 or #10). Poke the tip into the bottom of each puff and fill with the pastry cream, being careful not to overfill. Refill the pastry bag as needed. Have a large bowl of ice water ready. Put the sugar and salt in a 3-quart heavy-duty saucepan. Add 2/3 cup water and swirl to moisten the sugar. Cover and boil over high heat until starting to turn golden around the edges, 5 to 7 minutes. Remove the lid and cook, swirling occasionally, until the caramel is light golden, 1 to 2 minutes more. Immediately put the bottom of the pot in the ice water to stop the cooking. Remove the pot from the water and put it on a heatproof surface. Have a small bowl of ice water nearby. Put the foil-wrapped cone on a serving platter. Insert a toothpick about 1 inch from the base of the cone. Dip the side of a large cream puff into the hot caramel to coat the side and about a third of the top of the puff. Immediately press the cream puff onto the toothpick, with the top facing out. Insert another toothpick parallel to the first pick, positioning it so that the next puff will fit snugly against its neighbor. Dip another cream puff and nestle it against the first. Repeat, making your way up and around the cone, working from the largest to the smallest puffs. If you get any hot caramel on your fingers, immediately dip them into the ice water to stop the burn. As the caramel cools and thickens, it will begin to spin into long, thin threads as you pull the puffs from the pot. Before attaching the puff, circle the cone with the puff so the spun caramel drapes the croquembouche. When the caramel becomes too thick to dip, swirl it over low heat to thin it—it will darken a little each time you do this. When the cone is completely covered with puffs, dip a fork into the caramel and continue to pull the caramel threads from the pot and spin them around the croquembouche until you’re happy with its appearance. Serve any extra cream puffs on the side.