Wait to preheat the oven until you chill the cookie dough. Line two large baking sheets with silicone baking mats or parchment paper. Set aside.
In a large bowl or the bowl of a stand mixer, beat 1 cup or 2 sticks of butter, 1/2 cup granulated sugar, and 1/2 cup of packed light brown sugar at a medium-high speed with a hand mixer or whisk attachment. Beat for a couple of minutes, until the mixture becomes lighter in color.
Add 1 egg + 1 large egg yolk, 2 Tbsp maple syrup, 2 tsp vanilla extract, and 2 tsp maple extract. Mix on a medium speed until incorporated.
Then mix in 2 3/4 cups flour, 1 1/2 tsp baking powder, and 1/2 tsp fine salt on a low speed until just combined and there are no longer any visible streaks of flour. Scrape the sides of the bowl with a rubber spatula between additions.
At this point, the dough should still be pretty sticky. Divide the dough in half and wrap each portion of dough in a piece of plastic wrap. I like to flatten the dough out into a rectangle that's about 1/2 inch tall to make it easier to roll out once it's chilled.
Chill the dough in the fridge for 1 hour, in the freezer for 20 minutes, or in the fridge overnight.
Turn on the oven to 350°F/175°C for about 30 minutes before you plan to roll out the dough.
Take one piece of dough out of the fridge or freezer, leaving the other in there to continue to chill. Unwrap the cookie dough and lay the plastic wrap out flat on your counter. We will be rolling out the cookie dough on the plastic wrap to make cleanup a breeze and to make it easier to cut out the cookies. Dust both sides of the cookie dough, your rolling pin, AND the cookie cutter with flour. Roll out the dough to be about 1/4 of an inch thick. If they're any thicker, your sandwich will end up being super thick!
Use a maple leaf cookie cutter to cut out as many cookies as possible and place them about 1 inch apart on the prepared sheets. They don't spread much as they bake, so you can place them pretty close together.
Chill the cut-out cookies one more time in the fridge for 15 minutes or the freezer for 5 minutes to help them keep their shape as they bake.
Bake one sheet of cookies at a time for 12-14 minutes on the middle rack of your oven for crunchy cookies. If you want them to be soft and chewy, bake for 11-12 minutes. Keep in mind that bake time can vary based on the size of the cookies and the thickness of your dough. Keep a close eye on the cookies and be sure to pull them out before the edges start to brown.
Let the baked cookies cool on the pan for about 15 minutes, then transfer to a wire rack to finish cooling. While the first batch bakes and cools, knead together the cookie dough scraps and repeat the above steps. Repeat this process with the remaining dough.