Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
Cream the softened butter and granulated sugar together in a large bowl until the mixture is pale and fluffy.
Beat in the egg and vanilla extract until fully incorporated, scraping down the sides of the bowl as needed.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture and mix until just combined.
Roll the dough into small balls and place them on the prepared baking sheet.
Use your thumb to create a shallow indentation in the center of each cookie.
Fill each indentation with about a teaspoon of strawberry jam.
Bake for 12 minutes or until the edges are lightly golden.
Let the cookies cool completely on a wire rack.
Whisk together the powdered sugar and milk to create the icing.
Drizzle the icing over the cooled cookies and top with sprinkles if desired.