To make the cookies:
Preheat oven to 375 degrees. Line two baking sheets with parchment paper.
Cream butter and powdered sugar together in the bowl of a stand mixer fitted with the paddle attachment. Add the de and the extracts, scraping the sides of the bowl as needed until everything is combined. Gradually add the flour and salt. Beat the dough until it comes together.
Turn dough out onto a floured work surface and roll dough to a 1/4 inch thickness. *There is no leavening in this recipe (to maintain shape and detail from the cookie cutter), so the thickness will remain about the same after baking. Be careful not to roll too thin. Cut with cookie cutters and carefully transfer to baking sheets.
Bake for 8 minutes, or until set but not browned. Allow to cool 5 minutes before transferring to a cooling rack. Frost when cool.
To make the frosting:
Cream butter in the bowl of a stand mixer fitted with the paddle attachment. On low speed, gradually add the powdered sugar sugar. Add the almond and vanilla extracts and half and half gradually. Beat the frosting until fluffy and smooth. (Add food coloring here, if using).
Spread or pipe the frosting onto cooled cookies. Add sprinkles, as desired. Store cookies in a single layer in a covered container at room temperature.