Mix flour, butter, and 1/2 cup sugar together in a bowl using your hands until dough is well combined. Press dough into an ungrased 11 1/2x 7 1/2-inch pan or jelly roll pan. Sprinkle with 1 tablespoon sugar.
Bake in the preheated oven until edges are light brown, 20 to 30 minutes. Cut shortbread into squares in the pan while still warm. Cool completely before removing squares from pan.
2 1/2 cups all-purpose flour
1 cup butter, at room temperature
1/2 cup white sugar
1 tablespoon white sugar, or as needed