1. Preheat oven to 350° degrees. Line a large baking sheet with a Silpat mat or spray with non stick spray.
2. In a small bowl, stir strawberries, lemon juice and 1 tablespoon sugar until combined. Let sit 10 minutes, then drain.
3. In a medium bowl, whisk together flour, baking powder, and salt. Set aside. In a mixer, beat butter, remaining ½ cup sugar, and brown sugar until light and fluffy. Beat in egg and vanilla extract, then slowly mix in in flour mixture until just combined. Using a wooden spoon, very gently fold in strawberries. Set aside.
4. In a medium bowl, mix cream cheese, powdered sugar, and lemon zest until smooth. Using a medium cookie scoop, scoop heaping tablespoons of dough and flatten into pancake-like circles on the baking sheet. Place cream cheese filling on top of pieces of dough. Place remaining dough on top of filling and pinch edges together. Roll gently into balls.
5. Arrange stuffed cookie dough balls 2″ apart on baking sheets and bake until cookies are set and just golden around edges, about 18 minutes.