Make the crust: Whisk together flour, cocoa powder, baking powder, baking soda, and salt in a large bowl. With an electric mixer on medium-high speed, beat butter and both sugars until fluffy, 3 to 4 minutes. Beat in yolk and vanilla. Reduce speed to low; mix in flour mixture, scraping sides of bowl as needed.

Preheat oven to 350 degrees. Press dough evenly into bottom of a 10-inch springform pan to form a 1/4-inch-thick crust. Chill in freezer 15 minutes. Bake until firm, about 15 minutes. Transfer pan to a wire rack, and let cool completely. Leave oven on.

Make the filling: Whisk together granulated sugar, flour, and cocoa powder. Beat cream cheese with an electric mixer on medium speed until fluffy, about 3 minutes, scraping sides of bowl as needed. Reduce speed to low. Gradually add the sugar mixture, and mix until smooth. Add sour cream and vanilla, and mix until smooth. Add whole eggs, 1 at a time, and the yolk, mixing just to combine after each addition. Add chocolate, and mix until combined.

Wrap exterior of springform pan with a double layer of foil. Pour filling onto prepared crust, and set springform pan in a roasting pan. Fill roasting pan with enough boiling water to reach halfway up the sides of springform. Bake cheesecake 45 minutes.

Reduce oven to 325 degrees. Continue to bake until set but slightly wobbly in the center, about 30 minutes more. Turn oven off; leave cake in oven with door ajar for 1 hour.

Transfer springform pan to a wire rack, remove foil, and let cake cool completely. Run an offset spatula or a knife around edge of cake, and carefully unmold. Set cake on wire rack set over a rimmed baking sheet.

Make the glaze: Combine chocolate and corn syrup in a heatproof bowl. Bring cream to a boil in a small saucepan; pour over chocolate mixture. Let stand 5 minutes, then whisk until smooth. (Do not whisk too much or bubbles will form.) Let cool 10 minutes. Pour glaze over cake in a circular motion, starting at the center and slowly moving outward toward the edge, to cover entire surface. Refrigerate, uncovered, until set, at least 4 hours (or up to 2 days, covered).

Decorate the cake: Print snake stencil template. Place it under a sheet of calendar vinyl. Use a permanent marker to trace the outline and the snake design onto vinyl. Working on a cutting mat, use a craft knife to cut along the lines. Work slowly and carefully. The vinyl will dull the knife's blade; change the blade as necessary. Set snake stencil on cake. Sift green powdered food coloring over snake, avoiding the tongue. Sift red powdered food coloring over tongue. Carefully remove stencil. Serve immediately.