In a stand mixer with the paddle attachment, beat the butter, coconut oil and sugar until combined and fluffy.
Add the eggs, vanilla extract, and almond extract. Stir to combine, scraping down the sides of the bowl to incorporate all the ingredients.
Add the flour, baking powder and sea salt and mix with the paddle attachment for about 2-3 more minutes, or until a soft dough is formed.
Remove the mixing bowl from the stand mixer and scrape all the dough into a ball. Cover the bowl with plastic wrap and refrigerate for 1 hour.
Preheat the oven to 350℉.
Dust a work surface and rolling pin with flour. Remove about 1/4 of the dough from the bowl to roll out. Return the rest of the dough to the refrigerator until the first set of cookies are rolled out.
Roll the dough to about 1/4 inch thick, adding more flour if the surface or the rolling pin get sticky. Cut out as many shapes with the cookie cutter as possible and place onto a parchment paper lined baking sheet. Reroll the dough and continue cutting out until all the dough is used.
Once one sheet pan is full (about a dozen cookies) bake in the preheated oven for 10 minutes.
Allow the cookies to remain on the hot sheet pan, on a cooling rack for 3 minutes after removing from the oven.
Transfer the cookies to a cooling rack and allow to fully cool (at least 30 minutes) before frosting.
Once the cookies are cooled and frosted, store in an airtight container at room temperature for up to one week.