Center a rack in the oven and preheat to 400 (F). Prepare two sheet pans by lining with parchment paper and set aside.
In a small bowl, combine 1 1/2 cups minus 1 tablespoon granulated sugar, 1 tablespoon dark brown sugar, and fresh zest from a medium lemon. Use your fingers to toss the ingredients together until combined, and rub the zest into the sugar until it starts to clump and smell fragrant — this helps release oils from the zest that infuse the sugar and makes your cookies tastier. Set aside.
In a medium bowl, combine 2 3/4 cups all-purpose flour, 2 teaspoons cream of tartar, 1 teaspoon baking soda, and 2 teaspoons kosher salt. Whisk until well combined and set aside.
In the bowl of a freestanding electric mixer fitted with a paddle attachment, combine 1 cup unsalted butter and the sugars from the 2nd step. Beat on medium-high speed for about 2 to 3 minutes, until light and fluffy. Reduce the mixer speed to its slowest setting and add 2 large eggs, one at a time, only adding the next egg when the previous one is fully incorporated. Add 1/2 teaspoon lemon extract. Once incorporated, stop the mixer and use a rubber spatula to scrape down the sides of the bowl. Turn the mixer back on to its lowest setting and gradually add the dry ingredients, beating on low speed until just combined. Use a 3-tablespoon cookie dough scoop to measure out cookie dough balls and place them on the lined sheet pans at least 3 inches apart. Before baking, roll each cookie dough ball in the Raspberry Sugar Coating and transfer back to the sheet pans. Transfer one sheet pan to the preheated oven and bake for at least 10 minutes, until the edges are set but the centers are puffed and gooey. Transfer to a wire rack to cool for at least 10 minutes, before using a metal spatula to turn each cookie out onto the rack to cool completely. Repeat with the remaining tray.