01 - Preheat oven to 350°F. Line two baking sheets with parchment paper.
02 - Whisk together flour, baking powder, and salt in a medium bowl; set aside.
03 - Using an electric mixer, beat softened butter and granulated sugar until light and fluffy, about 3 minutes.
04 - Add the egg and vanilla extract to the creamed mixture; mix until fully combined.
05 - Gradually add the dry mixture to the wet ingredients, stirring until just combined to avoid overmixing.
06 - Scoop tablespoon-sized portions of dough onto prepared sheets, spacing 2 inches apart.
07 - Bake for 9 to 11 minutes or until edges turn lightly golden. Avoid overbaking to maintain softness.
08 - Let cookies cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
09 - Melt butter in a saucepan over medium heat. Stir in brown sugar and salt until dissolved and bubbling, approximately 2 minutes.
10 - Whisk in milk and bring to a gentle boil; remove from heat and let cool for 5 minutes.
11 - Gradually whisk in sifted powdered sugar and vanilla extract until smooth and spreadable; adjust consistency with milk if necessary.
12 - Spread caramel frosting over cooled cookies evenly and allow frosting to set before serving.