Strawberry Cheesecake Cookies

Name: Strawberry Cheesecake Cookies
Prep time: 40 min
Cook time: 10 min
Total time: 50 min
Cuisine: American
Ingredients: 3½ cups flour; 1 tsp baking powder; ¼ tsp salt; 1 cup unsalted butter, at room temperature; 8 oz cream cheese, at room temperature ((I used full fat)); 1½ cups sugar; 1 egg, at room temperature; 1 tsp vanilla bean paste ((see note)); ½ cup unsalted butter, at room temperature; 1 tsp strawberry extract ((see note; optional)); pinch salt; 0.8 oz freeze-dried strawberries ((one bag; see note)); 4 cups powdered sugar, sifted