In a large bowl add flour, baking powder, and salt, and whisk together to combine. In the bowl of an electric mixer, add butter and sugar and beat together on medium-high speed until soft and fluffy, about 2-3 minutes. Beat in eggs one at a time, mixing well after each addition and scraping down bowl as needed. Add vanilla and mix until just combined.
Add dry ingredients and mix on low speed until just combined and no flour pockets remain. Cover dough with plastic wrap and chill for 1 hour.
Move oven rack to the middle position, and preheat to 350˚ F. Line cookie sheets with parchment paper or silicone baking mats, and set aside.
Scoop 3 tablespoons of dough and roll into a ball. Place on prepared cookie sheets and flatten ball slightly with the palm of the hand. Repeat with remaining dough, spacing cookies at least 2-3 inches apart. Bake one cookie sheet at a time and bake about 10-12 minutes or just until set, and do not overbake! The edges of the cookies will be lightly browned. Cool cookies on cookie sheet for 5 minutes and then transfer to a wire rack to cool completely. Repeat with remaining dough.
MAKE THE FROSTING:
In a medium bowl add powdered sugar, melted butter, vanilla, and milk. Whisk until smooth, whisk in additional milk as necessary, 1 teaspoon at a time, until desired consistency is reached. Color with pink food coloring if desired.
Frost cookies by adding a dollop of frosting to the center of the cookie, and use offset spatula or spoon to smooth out to edges.
If frosting begins to thicken as you decorate, just continue to whisk in very small amounts of milk to keep it workable. Top with sprinkles if desired.
STORE THE COOKIES:
Let frosting set for 2 hours before storing. Store in an airtight container at room temperature for up to 4 days.