Remove as much moisture from pumpkin puree as possible by pressing between paper towels until it can hold its shape if squeezed into a ball, and set aside.
Whisk dry ingredients (flour, cornstarch, and pumpkin pie spice) together and set aside.
Cream butter and sugars with paddle attachment, on medium-low speed, until fluffy and pale in color (about 5 minutes).
Add egg, extract, emulsion, and pumpkin puree and mix on low speed until thoroughly combined. Scrape down the paddle with a spatula, and then continue to mix on low speed for another 30 seconds to ensure everything is fully incorporated.
Add dry ingredients, all at once, and mix on low speed just until dough starts to come together and no dry bits remain. Do not overmix.
If making cut-out cookies: turn dough out onto cling wrap, tightly wrap, and refrigerate overnight (or for at least 4 hours). If making slice-and-bake cookie: divide dough in half, roll into logs, and wrap tightly in cling wrap or wax/parchment paper, and refrigerate until firm.
If making cut out cookies: knead, roll, cut out cookies, and return to fridge or freezer until firm. Leave a couple inches between cookies. If making slice-and-bake cookies: slice ¼” cookies.
Bake at 350°F for 15 minutes, rotate pan, and bake for another 1-5 minutes until edges are starting to darken.
Remove cookies from oven and allow to cool on cookie sheet.