In a large mixing bowl, combine softened butter, granulated sugar, and cornstarch, blending thoroughly. Add the maple flavoring and mix well. Gradually incorporate the flour, blending until a smooth dough forms.
Shape the dough into a flat disk and cover with plastic wrap. Chill in the refrigerator for approximately 45 minutes, or until the dough is firm enough to roll out.
Preheat the oven to 325°F. Lightly flour a work surface, and roll the dough to a thickness of 1/4 inch. Using a floured leaf-shaped cookie cutter (approximately 2-3/4 inches), cut out shapes. Place the cookies 1 inch apart on parchment-lined baking sheets.
Bake for 20-25 minutes, or until the edges turn a light golden brown. Transfer cookies to wire racks to cool completely.
In a small bowl, whisk together the confectioners' sugar and maple syrup until smooth. Spread the glaze over each cookie and allow it to set fully before serving.