Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats.
In a large bowl, use an electric mixer (or a sturdy spoon) to beat the 1 cup (2 sticks) salted butter at room temperature and 1/2 cup powdered sugar together until pale and creamy, scraping down the sides of the bowl as needed.
Add the 2 cups all-purpose flour to the butter mixture a little at a time, mixing on low until the dough comes together and no dry streaks of flour remain.
Turn the dough onto a well-floured surface and gently knead once or twice to form a smooth disk. Roll the dough to about 1/4-inch (6 mm) thickness.
Scatter colored sprinkles over the top of the rolled dough and press them lightly into the surface so they adhere.
Use a round cutter to cut cookies; press straight down (do not twist) and transfer the cut cookies to the prepared baking sheets. Place them fairly close together—these cookies will not spread much.
Re-roll the dough scraps, roll to 1/4-inch thick, press more sprinkles into the top, and cut the remaining cookies.
Bake the cookies for 18 to 22 minutes, or until they are just lightly golden at the edges.
Let the cookies cool on the baking sheets for about 5 minutes, then transfer them to a wire rack to cool completely.