1. Preheat oven to 350 degrees. Butter two 9-inch square cake pans; line bottoms with parchment paper. Butter parchment, and dust with cocoa; tap out excess. Set aside.

2. Into a mixer bowl, sift together cocoa, flour, granulated sugar, baking soda and powder, and salt. Add eggs, warm water, buttermilk, oil, and vanilla. Mix on low speed until smooth, about 2 minutes, scraping down sides of bowl as needed.

3. Divide batter between prepared pans, and smooth tops. Bake until a tester inserted near the center comes out clean and center of cake is springy to the touch, 35 to 40 minutes. Transfer pans to a wire rack; let cool 15 minutes before inverting cakes onto rack. Let cool completely.

4. Trim tops of cakes to make level. Spread a thin layer of chocolate buttercream over cakes to seal in crumbs; refrigerate until firm, about 20 minutes. Using an offset spatula, spread another layer of chocolate buttercream over cakes, squaring the corners and smoothing the tops completely. Chill until set, about 30 minutes.

5. Decorate star square: Cut out a paper star; place on top of cake. Sprinkle sanding sugar around star, covering cake; remove star template. Use a pastry bag fitted with an Ateco #5 plain tip to pipe an oval in the bottom center of the star for the camera, leaving enough room to pipe writing above. Use licorice candies to make the camera.

6. Pipe borders of both cakes: Using yellow buttercream and #5 tip and light-brown buttercream and Ateco #16 star tip, pipe alternating dots and stars on top edge.

7. Decorate handprint square: Set cookie handprints on lower half of cake, extending over the edge. Using a pastry bag fitted with an Ateco #3 plain tip and filled with pink buttercream, write the birthday-girl's name above handprints. Pipe "happy birthday" on star cake, above the camera. Arrange cakes next to each other to resemble two sidewalk squares.