In a large bowl or the bowl of a stand mixer, beat 3/4 cup butter and 1/2 cup cream cheese on medium speed with a hand mixer or whisk attachment until smooth.
Next, add in 1 1/2 cups granulated sugar and mix on a medium-high speed for a couple of minutes, until the mixture becomes lighter in color.
Add in 1 egg, 2 tsp vanilla bean paste or vanilla extract, and 1 tsp almond extract (optional). Mix on a medium speed until incorporated.
In a separate bowl, whisk together 3 cups flour, 1 Tbsp cornstarch, 1 tsp fine salt, and 1/2 tsp baking powder. Add the flour mixture into the butter mixture and mix on a low speed until it is JUST incorporated. Scrape the sides and bottom of the bowl with a rubber spatula to make sure everything is properly mixed together.
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 about 2 hours, in the freezer for 30 minutes, or in the fridge overnight. If you chill the dough overnight, let it sit out at room temperature for about 10 minutes before trying to roll it out. This will make it easier to roll out!
Preheat the oven to 350°F/175°C for about 30 minutes before you plan to roll out the dough, and line two large baking sheets with silicone baking mats or parchment paper. Set aside.
Take one piece of dough out of the fridge, 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 and your rolling pin with flour.
Roll the chilled dough to be 1/3 inch thick and cut out shapes with a flour-dusted cookie cutter. Use a kitchen brush to brush any excess flour off the cookies and place them on the prepared baking sheets. The cookies don't spread much as they bake, so you can place them about 1 inch apart.
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. Bake for 10-13 minutes on the top rack of your oven (bake time will vary based on the size and shape of the cookies). 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 rewrap them in plastic wrap. Pop them back in the fridge to chill.
Pull out the 2nd chilled portion of dough and repeat steps 8-12. Then repeat with the chilled dough scraps.