Preheat the oven to 375°F and prepare two baking sheets with parchment paper. Combine the butter, ½ cup powdered sugar, and vanilla in a large bowl and beat with an electric mixer until the mixture becomes light and fluffy. Gradually add the flour and salt, mixing until a cohesive dough forms. Gently fold in the sprinkles. If the dough feels overly soft, refrigerate briefly until firm enough to handle. Scoop balls of dough measuring 1 or 2 tablespoons and arrange them on the lined baking sheets. Bake for 7–10 minutes for smaller cookies or 10–14 minutes for larger ones, until the undersides are lightly golden. Let the cookies rest for 5 minutes before rolling them generously in powdered sugar. Transfer to a cooling rack and, if desired, coat once more with powdered sugar once fully cooled.