Preheat the oven to 350°F (175°C). Grease a 12-cup muffin tin or line with paper liners.
In a large bowl, cream together 1 cup softened unsalted butter and 1 cup granulated sugar until light and fluffy, about 3-4 minutes.
Add 1 large egg and 1 teaspoon vanilla extract to the butter mixture and beat until combined.
In a separate bowl, whisk together 2 1/4 cups all-purpose flour, 1/2 teaspoon baking powder, and 1/4 teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined to form the cookie dough.
Divide the cookie dough evenly among the 12 muffin cups, pressing the dough into the bottom and up the sides to form a cup shape.
Bake the cookie cups for 12-15 minutes, or until the edges are lightly golden. Remove from the oven and set aside.
While the cookie cups bake, prepare the lemon filling. In a medium bowl, whisk together 3 large eggs, 1 1/2 cups granulated sugar, 1/4 cup all-purpose flour, 1/2 cup freshly squeezed lemon juice, and 1 tablespoon lemon zest until smooth and well combined.
Pour the lemon filling evenly into each pre-baked cookie cup, filling almost to the top.
Return the muffin tin to the oven and bake for an additional 12-15 minutes, or until the lemon filling is set and slightly firm to the touch.
Remove from the oven and allow the cookie cups to cool completely in the tin on a wire rack.
Once cooled, carefully remove the cookie cups from the muffin tin and dust the tops lightly with powdered sugar before serving.