Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

Sift flour, baking powder, and salt together in a bowl.

Beat ½ cup butter and white sugar in a large bowl using an electric mixer until smooth. Beat in eggs, one at a time, then mix in ½ cup maple syrup and maple extract. Stir in the flour mixture until dough forms, then fold in walnuts.

Divide dough in half. Shape each half into a log and flatten into a rectangle 3-inches wide and 1-inch tall. Place on the prepared baking sheet.

Bake in the oven until lightly browned, about 30 minutes. Remove from oven and cool for 15 minutes but keep the oven on.

Slice logs diagonally into ½-inch-thick slices. Lay slices on their sides on the baking sheet.

Bake again until lightly browned and crisp, about 8 minutes. Cool for 3 to 5 minutes.

Make the glaze: Combine ¼ cup maple syrup and 1 tablespoon melted butter in a bowl. Gradually stir in confectioners' sugar until smooth.