Preheat oven to 350 degrees F.
In a stand mixer bowl, cream butter, sugar, and lemon zest with the paddle attachment until light and fluffy, about 3-5 minutes.
Add eggs one at a time, mixing on low speed and scraping the bowl between each addition. Then add vanilla extract and salt; mix just until combined.
In a separate bowl, whisk together baking powder, baking soda, and flour.
Add the flour mixture to the butter mixture and mix on low speed until just combined.
Use an ice cream scoop to form 1-inch balls. Place dough balls in a greased mini muffin tin and press the other end of the scoop into the center to create a cup shape.
Bake for 7-8 minutes until edges are lightly golden.
Allow cookie cups to cool for 5 minutes in the tin, then transfer to a wire rack to cool completely.
For the lemon curd, blend lemon juice, egg yolks, sugar, cornstarch, and lemon zest until smooth.
Pour the mixture into a saucepan and cook over medium heat, stirring constantly until it reaches a rapid boil or about 172 degrees F.
Remove from heat and whisk in cold cubed butter until smooth.
Spoon 1 tablespoon of lemon curd into each cooled cookie cup.
Chill the filled cookies in the refrigerator until set.
Optionally, sprinkle with powdered sugar before serving and enjoy.