Make the cake
Preheat the oven to 350ºF. Grease an 8-inch square baking pan and dust it with flour, knocking out any extra. Combine the graham cracker crumbs, flour, baking powder, and salt in a medium mixing bowl.
Combine the butter and sugar in a large mixing bowl and cream with an electric mixer on medium-high speed until fluffy, about 3 minutes, scraping down the sides of the bowl as necessary. With the mixer on low speed, add the egg, egg yolk, and vanilla. Scrape down the sides of the bowl and then beat until smooth.
With the mixer on low speed, add 1/3 of the flour mixture, then 1/2 of the milk, stirring until combined. Repeat with the remaining flour and milk, ending with the flour. Stir in the chocolate chips.
Scrape the batter into the prepared pan and smooth the top with a rubber spatula. Bake until a toothpick inserted in the center comes out clean, about 35 minutes. Let the cake cool in the pan for about 10 minutes. Invert it onto a wire rack, and then turn it right side up on a rack to cool completely.
Make the frosting
Place the butter in a medium mixing bowl and beat until creamy. With the mixer on low speed, slowly add the sugar, scraping down the sides of the bowl as necessary. Stir in the vanilla and the Marshmallow Fluff and beat until smooth.
Cut the cake into squares and serve each one with a dollop of frosting on top.
Make Ahead Tips
Store uneaten squares in a cake keeper or wrap in plastic and store at room temperature for up to 3 days. The frosting can be kept in the refrigerator in a bowl covered with plastic wrap for up to 3 days. Bring to room temperature before using.
Photo: Alexandra Grablewski