For the brownie: Preheat the oven to 350 degrees F. Grease a 9 x 13-inch metal baking pan. Line the bottom and two sides of the pan with parchment paper (leave an overhang to make it easier to take out of the pan). In a medium bowl, whisk together the sugar, flour, cocoa powder, baking powder, and salt. Add the oil, milk, vanilla, and egg. Whisk until well combined. Pour the batter into the prepared pan and spread evenly. Bake until a wooden pick inserted in the center comes out mostly clean, 20 to 25 minutes. Let cool completely in the pan.
For the butter cake cupcakes: Preheat the oven to 350 degrees F. Line 24 cups of 2 muffin tins with paper liners. (Or use 1 muffin tin and bake in two batches.) In a large bowl, whisk together the flour, almond meal, baking powder, and salt. Set aside. In a second large bowl, with an electric mixer, beat the butter until softened. Add the superfine sugar and beat until light and fluffy, 3 to 5 minutes. Scrape down the sides of the bowl as needed. Beat in the vanilla. Add the eggs, one at a time, beating well after each addition. Scrape down the sides of the bowl as needed.
On low speed, alternate adding the flour mixture and the milk to the butter mixture, beginning and ending with the flour mixture.
Fill the cupcake liners two-thirds full with batter. Bake until a wooden pick inserted in the center of a cupcake comes out clean, 18 to 20 minutes. Transfer to a wire rack to cool. Let the cupcakes cool completely before decorating.
Assemble the burgers: Use the round cookie cutter to cut out "hamburger patties" from the brownies. Halve the cupcakes horizontally with a straight edge (not serrated) knife. Place the brownie burgers on the bottom halves of the cupcakes.
Decorate the cupcakes: Mix half of the buttercream frosting with yellow food coloring until it is the color of cheese. Scoop the frosting into a decorating bag fitted with a #48 tip and pipe it to look like cheese slices on your patties. Tint the other half of the buttercream frosting with red food coloring until you reach the desired shade of bright red. Scoop the frosting into a decorating bag fitted with a #10 tip and pipe it to look like a tomato on top of the cheese. Mix the flaked coconut with liquid green food coloring until it is light green, resembling lettuce. Sprinkle the coconut flakes on top of the red frosting. Place the top half of each cupcake on top. Scatter white sprinkles on top of the cupcakes to look like sesame seeds. Use baking tweezers for more control.