Preheat the oven to 350° and spray a mini muffin pan(s) with non-stick cooking spray.
In a large bowl, mix butter, sugar, brown sugar, rum extract, and eggs together until combined.
In a separate bowl, whisk together flour, baking soda, baking powder, and salt.
Slowly add dry ingredients into wet ingredients and mix on medium speed until just combined.
Roll dough into ½ inch balls and press firmly into the bottom of the muffin pan.
Bake for 15-17 minutes until edges are golden brown and the middle of the cookie is fully set.
Take the end of a spatula and press into the middle of each cookie to create a cup for filling.
Let sit in the muffin pan for 10 minutes, then transfer to a wire rack and cool completely.