Prepare the filling first by beating cream cheese and 2 tablespoons butter until smooth. Add 1 cup powdered sugar, 1 tablespoon lemon juice and 1 tablespoon zest, mixing until combined. Cover and refrigerate.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, cream ¾ cup butter and granulated sugar until light and fluffy, about 2-3 minutes.
Add egg, 2 tablespoons lemon zest, 2 tablespoons lemon juice, and vanilla to the butter mixture, beating until well combined.
Gradually add the flour mixture to the wet ingredients, mixing just until combined.
Chill the dough for 30 minutes.
Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Using a tablespoon measure, scoop dough and roll into balls.
Make an indentation in each cookie using your thumb or the back of a measuring spoon.
Fill each indentation with about ½ teaspoon of the chilled lemon cream cheese filling.
Bake for 10-12 minutes until the edges are just barely golden.
Cool completely on wire racks before dusting with powdered sugar.