Prepare the dry ingredients: Sift 4 1/2 cups of all-purpose flour into a separate large bowl. With a zester, zest the lemon and add the lemon zest to the bowl with the flour. Add the baking powder and salt. Combine flour, lemon zest, baking powder, and salt together. Set aside.
Whip the butter: Add 2 cups of unsalted, softened butter to a large mixing bowl. Use the paddle attachment and an electric stand mixer. Beat the butter on a medium-low setting for 5 minutes (setting #4 on the KitchenAid stand mixer). If the butter isn't fluffy, then it may need to warm up slightly at room temperature, or it may need to be mixed on a higher setting.
Mix in the eggs: After 5 minutes, the butter should be light and fluffy. Use a spatula to scrape down the sides of the mixing bowl and the paddle. Add the icing sugar and mix the icing sugar and butter on medium speed (#4 on a KitchenAid mixer) for 2 minutes. Lightly whisk the egg yolk, vanilla, and brandy in a separate bowl. Slowly add the egg mixture to the butter and mix on medium speed for 30-45 seconds or until the egg is incorporated. At this point, you can add the almond extract if you'd like to include more almond flavour in your cookies. Turn off the mixer until you're ready to add the flour. Preheat your oven to 350°F on bake.
Bake the almonds: While the oven is preheating, spread the slivered almonds on a small baking tray. Leave the almonds in the oven for 5-10 minutes or until they're lightly toasted. Keep an eye on the almonds so that they don't burn. This step gives the almonds a little extra flavour, but you can skip this step if you'd like since the almonds will bake inside the cookies.
Mix in the flour: Add the flour mixture (flour, lemon zest, baking powder, and salt) to the butter mixture and slowly mix in the flour on a low setting (#2 if you're using a KitchenAid mixer). Continue to mix until the flour is just combined or you can no longer see the flour (be careful not to overmix). You can also remove the bowl from the mixer and continue mixing the cookie dough with your hands or a spatula until all the flour is absorbed.
Mix in almonds and cool the dough: Allow the almonds to fully cool (if you toasted them in the oven). Once cooled, add the lightly toasted almonds to the cookie dough. Mix together. The dough should be pliable enough to mold the cookies but not too soft that it sticks to your hands. If the dough is too soft, gradually add 1 tablespoon of flour to the cookie dough and continue to mix with your hands. Cover the cookie dough with saran wrap and allow the dough to cool in the refrigerator for 10-15 minutes.
Shape the kourabiedes: Remove the dough from the fridge, roll the cookie dough into 2" inch balls and place them on a cookie sheet. Lightly press down on the cookies to flatten them slightly before putting the cookies in the oven.
Bake the kourabiedes: Once the oven has preheated to 350 degrees F, place the cookies in the oven for 20-25 minutes or until a light golden brown colour. The baking time may need to be adjusted depending on the size of your cookies.
Cool and sprinkle with icing sugar: Remove the cookies from the oven on a heat-resistant surface and allow them to cool for a few minutes before placing them on a cooling wire rack. Let the cookies cool completely before dusting them with icing sugar. Once the cookies have thoroughly cooled, use a sifter and sprinkle the cookies with icing sugar. How much icing sugar you add can be up to you! Enjoy!