In a large bowl using a mixer fitted with the paddle attachment, cream together the ¾ cup unsalted butter and ¾ cup granulated white sugar on high speed until light and fluffy. This should take about 2 minutes.
Add the 1 egg yolk, 2 teaspoons vanilla extract, and ¼ teaspoon almond extract and mix until combined. Scrape down the sides of the bowl.
Add the ½ cup sourdough discard and mix until smooth. Scrape down the sides of the bowl.
Add the 2 cups all-purpose flour, ½ teaspoon baking powder, and ½ teaspoon kosher salt. Mix just combined being careful to not overmix.
Wrap the cookie dough in waxed paper and refrigerate for at least two hours.
Preheat the oven to 350°F (180°C).
Remove the dough from the refrigerator. On a lightly floured surface using a floured rolling pin, roll each piece out until it is ¼ inch thick. Any thinner and the cookies will be crispy instead of soft.
Use cookie cutters to cut out shapes and place them on a baking sheet lined with parchment paper. Gather up the scraps and roll them out again to cut out more cookies.
Refrigerate the cutout cookies for 15 minutes to help them keep their shape as they bake.
Bake the cookies for 11-12 minutes. You want to remove the cookies from the oven before they start to brown. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire cooling rack to cool completely.
Decorate using your favorite icing and decorations.
Notes
Measuring Ingredients: Using a digital kitchen scale is the most accurate way to measure your ingredients. If you don't have a kitchen scale you can measure the ingredients by volume but be careful when measuring the flour. Spoon the flour into the measuring cup and level it with the back of a butter knife. Try not to compress the flour into the measuring cup. Too much flour creates dense cookies.Salt: For all of my recipes, I use Morton Kosher Salt which packs more densely than Diamond Crystal Kosher Salt. If you are using Diamond Crystal Kosher Salt you will want to double the amount of salt you add.Butter: If you only have salted butter you will need to omit the salt in the recipe. There is about ¼ teaspoon of salt per stick of salted butter.No Cookie Cutters: After mixing the cookie dough, roll it into a log and wrap it in plastic wrap. Refrigerate the dough for at least 2 hours.When you are ready to bake cookies, unwrap the dough, slice it into ¼ inch slices and bake on a cookie sheet at 350°F (180°C) for 11 to 12 minutes.Quick Decoration: Sprinkle sanding sugar on top of the dough before baking.Cooling: Allow the cookies to cool for 5 minutes before transferring them to a wire rack. Let the cookies cool completely before decorating them. If you try to ice them when they are still warm the icing will melt. Storage: Baked cookies can be stored in an airtight container at room temperature for up to 4 days.