Special equipment: a 5.5-inch round cookie cutter and a 2.5-inch round cookie cutter
For the vanilla and chocolate cakes: Preheat the oven to 350 degrees F. Prepare four 9-inch cake pans with the nonstick cooking spray and dust with flour.
In a stand mixer fitted with a whisk attachment, add the granulated sugar and butter and cream together until combined, about 2 minutes. Add the eggs one at a time, beating to incorporate them. Add the baking powder, salt and 1 cup of the flour and continue to beat. Add the milk and remaining 2 cups flour, alternating back and forth. And the vanilla extract and beat for 1 more minute. Pour half of the batter into 2 of the prepared cake pans, reserving half to make into chocolate cake batter.
To make the chocolate batter, add the cocoa and hot water to a small bowl and mix to make a paste. Combine the chocolate paste with the remaining cake batter and mix until evenly combined. Pour the chocolate cake batter into the remaining 2 cake pans.
Place all 4 cake pans in the oven and bake until a toothpick inserted in the center of each comes out clean, 30 to 35 minutes. Let cool on a wire baking rack for 30 minutes.
For the vanilla frosting: In the bowl of a stand mixer fitted with a whisk attachment, add the confectioners' sugar and butter and mix on low speed for 1 minute until combined, then increase the speed to medium and beat until fluffy, another 3 minutes. Add the heavy cream and vanilla bean seeds and continue to beat for 1 more minute. Set aside.
To assemble checkerboard cake: To each cake, using a 5.5-inch round cookie cutter, cut out 1 ring, place a 2.5-inch round cookie cutter on the inside of the 5.5-inch ring to cut out a 2nd round. Repeat with the other 3 cakes. (This will give you 2 rings and 1 round per cake)
For the first layer: Place the largest yellow cake ring on your desired cake plate, place the second largest chocolate cake ring inside of the yellow cake ring, then place the smallest yellow cake round inside of the chocolate cake ring. Spread an even layer of vanilla frosting on top.
For the second layer: Place the largest chocolate cake ring on top of the first frosted layer of cake, place the second largest yellow cake ring inside of the of the chocolate ring, then place the smallest chocolate round inside of the yellow cake ring. Spread an even layer of vanilla frosting on top.
For the third and fourth layers, repeat the steps for the first 2 layers. Finish the top of the cake with an even layer of frosting, leaving the sides of the cake untouched.