Cream together butter and sugar in the bowl of a mixer fitted with the paddle attachment or using a hand mixer. Mix in eggs and extract.
In a separate bowl, whisk together the flour, baking powder, and salt. Add the flour mixture to the butter in batches, stirring until well combined.
Divide dough into four equal pieces, shape into discs, and wrap each in plastic wrap. Chill for at least 2 hours in the fridge, or 20 minutes in the freezer.
Preheat oven to 400°F.
Remove one disc from the fridge and roll the dough out on a floured surface until the dough is ⅛"-¼" thick.
Cut with cookie cutters (we recommend hearts of course!) and transfer to an ungreased cookie sheet. Bake for 6-8 minutes, watching closely. Cookies are done when bottoms are just barely golden. Remove cookies immediately from the baking sheet, and let cool completely on cooling rack before icing. Repeat with remaining dough, ensuring that the pans are cool to the touch before filling them with more cookie dough.
Decorate with sugar cookie icing (keep it as white icing or add a few drops of food coloring to dye it) and sprinkles, as desired.
Notes
The standard way to roll out sugar cookies is to use additional flour, but you can also use powdered sugar. The powdered sugar absorbs into the cookie while it bakes and doesn't leave any flour residue.