Add butter & both sugars to a stand mixer and cream together, using the paddle attachment, for 2-3 minutes on medium speed.
Add vanilla, almond extract, and eggs one at a time, mixing between additions. Mix just until everything is combined.
In a separate bowl, whisk together flour, baking soda, salt, and pumpkin pie spice.
With your mixer on low, gradually add the dry ingredients to the wet. Mix together until everything is well-blended and dough has an even consistency. (About 20-30 seconds mixing on low speed.) Your dough should be fairly creamy and not dry or crumbly.
If you're not going to chill the dough (you don't have to, but see the notes!), then preheat your oven to 350. Lightly flour the surface where you're going to roll your dough & cut the shapes.
Take a chunk of dough and work it with your hands, just to ensure it has an even consistency. Then roll the dough into a ball, roll the ball in the flour on the surface to give it a light coating, rub some flour on your rolling pin, and begin to roll the dough. You'll want to roll it until it's about 1/4 inch thick. If the dough is sticking to the surface or to your rolling pin, continue to add a little bit of flour until it's not sticky anymore.
Cut out your shapes, transfer them to your baking sheet (see notes on this, too!), and then re-roll the scrap dough into another ball, roll it out, cut shapes, etc. Continue until you've finished cutting all of the dough.
Place one baking pan in the oven and bake for 7 minutes at 350. (If you cut small shapes, you may want to just bake them for 6 minutes.)
Remove from oven and repeat with the other pan of cookie dough shapes.
Allow cookies to cool on the pan for about 5-10 minutes before transferring them to a cooling rack. Use a thin or metal spatula to transfer the cookies to lessen your chance of breaking them as you move them.
Once your cookies are fully cooled, it's time to ice them! See my notes for icing suggestions!