For the Cookies:
Preheat the Oven: Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
Mix the Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Cream the Butter and Sugar: In a large bowl, beat the softened butter and granulated sugar together using a hand mixer or stand mixer until light and fluffy, about 2-3 minutes.
Add the Wet Ingredients: Add the egg, vanilla extract, strawberry extract (if using), and strawberry puree. Mix until smooth and combined.
Combine with Dry Ingredients: Gradually add the dry ingredients into the wet ingredients, mixing until the dough comes together. If desired, add a few drops of pink food coloring for a more vibrant look.
Form the Cookies: Scoop tablespoon-sized portions of dough and roll them into balls. Place them on the prepared baking sheet, spacing them about 2 inches apart.
Bake: Bake for 10-12 minutes or until the edges of the cookies are lightly golden. The center should still be soft. Let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
For the Cream Cheese Frosting Drizzle:
Make the Frosting: In a bowl, beat the softened cream cheese, powdered sugar, vanilla extract, and a pinch of salt until smooth and creamy. Gradually add the milk, starting with 2 tablespoons, and continue to beat until you achieve a drizzling consistency.
Drizzle the Frosting: Once the cookies have cooled, drizzle the cream cheese frosting over the top of each cookie. You can use a spoon or place the frosting in a piping bag to create a more controlled drizzle.