In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl, cream softened butter and sugar until light and fluffy. Add egg and vanilla extract and mix until smooth. Stir in milk. Gradually add dry ingredients and mix until just combined. Fold in sprinkles evenly. Divide dough in half and shape into logs about 2 inches in diameter. Wrap tightly in plastic wrap and refrigerate for at least 2 hours or overnight. Preheat oven to 350°F and line baking sheets with parchment paper. Slice chilled dough into 1/4-inch thick rounds and place 2 inches apart on baking sheets. Bake for 10–12 minutes until edges are lightly golden. Cool on baking sheet for 5 minutes before transferring to a wire rack.