Preheat oven to 350 degrees. Line 2 standard muffin tins with cupcake liners; set aside.
Sift 2 cups plus 2 tablespoons sugar, flour, cocoa powder, baking powder, baking soda, and salt together into the bowl of an electric mixer. Using the paddle attachment, mix ingredients together on low speed.
In a large bowl, mix together eggs, milk, oil, and vanilla. Add to flour mixture and beat on medium speed for 30 seconds. Scrape down sides of bowl and continue mixing on medium speed for 2 minutes. Add boiling water and stir to combine; set cake batter aside.
Place graham cracker crumbs, remaining 1/4 cup sugar, and melted butter in a large bowl; stir until well combined.
Place 1 tablespoon graham cracker mixture into the bottom of each prepared muffin cup. Use the bottom of a small glass to pack crumbs into the bottom of each cupcake liner. Reserve remaining graham cracker mixture for topping.
Place 2 teaspoons chocolate in each muffin cup. Transfer muffin tins to oven and bake until the edges of the graham cracker mixture is golden, about 5 minutes. Remove from oven and fill each muffin cup three-quarters full with cake batter. Sprinkle each with remaining chocolate and graham cracker mixture. Return to oven and bake, rotating pans halfway through baking, until tops are firm and a cake tester inserted in the center comes out clean, 18 to 20 minutes. Transfer muffin tins to a wire rack and let cupcakes cool in pan for 10 minutes. Remove cupcakes from pan and let cool completely.
Place egg whites, sugar, and cream of tartar in the heatproof bowl of an electric mixer. Set over a saucepan with simmering water. Whisk constantly until sugar is dissolved and whites are warm to the touch, 3 to 4 minutes.
Transfer bowl to electric mixer fitted with the whisk attachment, and beat, starting on low speed, gradually increasing to high, until stiff, glossy peaks form, 5 to 7 minutes. Add vanilla, and mix until combined. Use immediately.
Transfer frosting to a large pastry bag fitted with a large plain round or French tip (such as Ateco #867 or Ateco #809). Pipe frosting in a spiral motion on each cupcake. Transfer cupcakes to a baking sheet. Using a kitchen torch, lightly brown the frosting, taking care not to burn the cupcake liners. Serve immediately or store in an airtight container, up to 2 days.