Combine butter, brown sugar, maple syrup, salt, and nutmeg in a bowl and beat with an electric mixer until smooth and combined, about 3 minutes. Add egg yolk, maple extract, and vanilla extract and beat until combined, about 1 minute. Add flour, cornstarch, and baking powder and mix until just combined.
Place dough onto a piece of plastic wrap and use the plastic wrap to help flatten it into a rectangle, about 1/2-inch thick. Wrap the dough up, and refrigerate for at least 2 hours, or up to 48 hours.
Remove dough from the fridge. Flour a work surface, and roll dough to 1/8-inch thick. Use a 2 1/2-inch maple leaf cutter (or any other shape) to cut out the shapes. Press dough scraps back together, and re-roll and re-cut dough as needed, until it is all used up. Place the cutout cookies into the refrigerator until chilled, about 30 minutes.
Preheat the oven to 350 degrees F (180 degrees C). Line 2 baking sheets with parchment.
Place cookies 1 inch apart on a prepared baking sheet. Keep remaining cookies in the refrigerator until ready to bake. If desired, use a sharp knife to score leaf vein shapes into the tops of cookies just before baking.
Bake 1 pan at a time in the preheated oven until just beginning to turn golden around the edges, 10 to 12 minutes. Allow cookies to cool on baking sheet for 5 minutes, then remove to a wire rack to cool completely.
For filling, beat together butter, confectioner’s sugar, maple syrup, maple extract, and pinch of salt together until completely smooth and combined, 2 to 3 minutes. Add in heavy cream and beat until mixture is light and fluffy, 2 to 3 minutes more. If frosting is too thin, add more confectioner’s sugar, 1 tablespoon at a time, until light, fluffy, and thick enough to spread.
Pipe or spread a small amount of frosting onto the bottom of one of the cooled cookies. Top with another cookie and gently press together. Repeat process with remaining cookies. Store cookies in an airtight container.