Preheat oven to 350 degrees with rack in center.
Prepare the batter: Place chocolate in a medium heatproof bowl, and set it over a medium saucepan of barely simmering water; stir chocolate until melted and smooth. Remove bowl from heat, and set aside to cool slightly.
Meanwhile, whisk together flour, baking powder, baking soda, and salt in a medium bowl; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar on medium speed, scraping sides of bowl as needed, until light and fluffy. On low speed, mix in melted chocolate. Increase speed to medium, and add eggs, one at a time, mixing well after each addition. Add vanilla, and beat until mixture is creamy and color has lightened slightly, about 1 minute. Mix in sour cream. On low speed, add half of reserved flour mixture, beating until just incorporated. Mix in 1/2 cup water. Add remaining flour mixture, and mix until just incorporated.
Line a cupcake pan with paper liners. Fill each liner with enough batter to come 1/8 inch from top, about 1/3 cup. Bake, rotating pans halfway through, until tops are firm and a cake tester inserted in the center comes out clean, about 20 minutes. Transfer cupcakes to a wire rack to cool in pan for 10 minutes.
Use a small knife to loosen any tops stuck to the pan. Carefully invert cupcakes onto the wire rack. Turn cupcakes right side up, and let cool completely.
Prepare the frosting: In a large heatproof bowl, combine sugar, 1/4 cup water, egg whites, and cream of tartar. Using a handheld electric mixer, beat on high speed until foamy, about 1 minute. Set bowl over a pan of barely simmering water. Beat on high speed until frosting forms stiff peaks, about 12 minutes; frosting should register 160 degrees.on a candy thermometer. Remove from heat; stir in vanilla and almond extracts, and beat for 2 minutes more until frosting thickens.
Transfer frosting to a large pastry bag fitted with a 1/2-inch plain pastry tip. Leaving a 1/8-inch border on each cupcake, pipe a spiral of frosting into a 2-inch-high cone shape, using about 1/2 cup of frosting per cupcake. Transfer cupcakes to a baking sheet, and refrigerate while preparing the chocolate coating.
Prepare the chocolate coating: Combine chocolate and oil in a medium heat-proof bowl set over a medium saucepan of barely simmering water; stir until melted and smooth. Transfer to a small bowl, and let cool about 15 minutes.
Holding each cupcake by its bottom, dip cupcake in the chocolate to coat frosting, allowing excess to drip off. Transfer to a baking sheet fitted with a wire rack. Spoon more coating around edge of cupcake and any exposed frosting; none of the frosting should show. Let cupcakes stand at room temperature 15 minutes.
Carefully remove paper liners from cupcakes, and discard. Place cupcakes on a serving platter, and refrigerate for 30 minutes to let coating set. Cover, and refrigerate for 2 hours more. Serve cold. Cupcakes can be refrigerated for up to 3 days.
