Heat the oven to 350°F and line a baking sheet with parchment. The oven should be fully hot before baking.

Mix the softened butter and sugar until smooth and light. The mixture should look creamy.

Add the egg and mix until fully blended. The batter should look even.

Stir in the flour, baking powder, and salt. Stop mixing when the dough comes together and looks soft.

Scoop the dough into even mounds and place them on the baking sheet. Lightly press the tops so they are thick but flat.

Bake until the cookies look set and pale, with no dark edges. They should feel soft when touched.

Let the cookies cool on the pan, then move them to a rack. They must be fully cool before frosting.

Beat the butter for the frosting until smooth. Add powdered sugar and salt, then mix in milk a little at a time.

Spread frosting on each cookie in a thick layer. Add sprinkles right away so they stick.