Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper to prevent sticking and help the cookies bake evenly.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, beat the softened butter and granulated sugar for about 2–3 minutes, until the mixture looks pale and creamy. Proper creaming helps create a tender cookie texture.
Add the egg and vanilla extract to the butter mixture. Beat until fully combined, scraping down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet mixture. Mix on low speed or stir by hand until a soft dough forms. If the dough is unusually dry or crumbly, add milk a teaspoon at a time until it comes together.
Cover the bowl and refrigerate the dough for approximately 30 minutes. This helps firm the butter and makes the dough easier to shape.
Scoop approximately 1 tablespoon of dough for each cookie and roll it into a ball. If desired, roll the balls in granulated sugar or colored sugar. Arrange them on the prepared baking sheets, leaving about 2 inches between each cookie. Gently flatten each ball slightly.
Bake for 9–12 minutes, until the edges are set and the bottoms are lightly golden. The tops may remain fairly pale. Avoid waiting for the entire cookie to turn brown, as overbaking can make sugar cookies dry.
Let the cookies rest on the baking sheet for 5 minutes before transferring them to a wire rack. Allow them to cool completely before adding frosting or sprinkles.
Serve the cookies plain for a classic buttery taste or spread a thin layer of vanilla frosting over each cooled cookie. Add sprinkles if desired. Enjoy with milk, tea, or coffee.