Use an electric mixer to combine 1 cup of butter, 2 cups of flour, 1/2 cup of powdered sugar, and 1/2 tsp of fine salt. The mixture might look a bit crumbly at first, but it will eventually form a soft dough once it's fully mixed. If the dough still won’t come together and you're using a microwave-safe bowl, microwave the bowl for 2–3 seconds at a time, just until the butter softens slightly. Don’t let it melt!
Once the dough has come together, mix in 3 Tbsp of rainbow nonpareil sprinkles until they're evenly distributed throughout the dough.
Scoop the dough on top of a large piece of plastic wrap and roll it out into a rectangle that's about 1/3 inch tall. Sprinkle the remaining 1 Tbsp of sprinkles over the top of the dough, and gently press the sprinkles into the dough to prevent them from falling off when we cut the dough later. Wrap tightly and place in the fridge for an hour, or until it's firm.
Preheat the oven to 350°F/175°C and line 2 large baking sheets with parchment paper or Silpat mats while the cookie dough chills. The cookies will spread less and keep their shape better on parchment paper, so I recommend using that if you have it.
Unwrap the cookie dough and lay the plastic wrap out flat on your counter. We will be cutting the cookie dough on the plastic wrap to make cleanup a breeze. Use a sharp knife to cut out small squares of dough that are about 1/2 inch. The cookies will spread a bit as they bake, so place them about 1 inch apart on the prepared pans.
Bake one tray at a time for 10–12 minutes, or until the cookies look set and the bottoms are lightly golden. Rotate the pan halfway through to help them bake evenly, then place the pan on a wire rack and let the cookies cool fully on the pan.