Preheat oven to 300 degrees F (150 degrees C). Line bottom and sides of an 8-inch square baking pan with parchment paper; crease corners well.

Whisk together 1 cup flour and 2 tablespoons confectioners' sugar; cut in 1/2 cup butter until mixture resembles fine crumbs. Pat mixture evenly into prepared pan.

Bake in the preheated oven for 20 minutes; remove to cool on a wire rack, about 15 minutes. Top base evenly with raspberry jam.

Preheat oven to 375 degrees F (190 degrees C).

Beat white sugar and 1/2 cup butter together until fluffy; beat in eggs until fluffy and pale yellow. Beat rice flour into egg mixture until well combined; stir in food coloring until batter reaches desired shade of red. Spread batter evenly over jam layer.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool completely in the pan; about 20 minutes.

Beat 2 cups confectioners' sugar and 1/3 cup butter together in a bowl with an electric mixer until smooth; stir in milk and maple extract. Spread icing evenly over cooled bars.

Hold edges of parchment paper; lift squares out of pan to a cutting board. Slice into 1-inch squares with a very sharp knife.