In a medium-sized mixing bowl, whisk together flour, baking powder, and salt. Set aside.
In a large mixing bowl, using an electric hand mixer with beaters attached, cream together the butter and sugar until light and fluffy, about 4-5 minutes. The mixture will be pale yellow and creamy.
To the butter mixture, mix in egg and vanilla extract until blended, about 1 minute.
Add the dry ingredients to the butter mixture (in Step 3), and mix until just combined.
Using a cookie scoop to scoop dough into muffin pans, flatten lightly.
Bake for around 12-14 minutes in the preheated oven until golden and mostly set.
Remove from oven and allow to cool for at least 7 minutes on a cooling wrack.
Loosen each cookie cup slightly by twisting them in the pan.
Gently remove them from the pan. Use a shot glass or a small jar to press firmly down in the center, creating a well. Set aside.