Preheat oven to 350°F and generously grease a mini muffin tray.
In a medium bowl, combine sugar cookie mix, softened butter, and egg. Mix well with a spatula or start mixing gently with a hand mixer on low.
Use a 1-tablespoon cookie scoop to drop dough balls into each muffin cup, filling 36 cups.
Bake for 10-12 minutes or until edges turn lightly golden brown.
Remove from oven and gently press into each cookie halfway down with a tart tamper or tablespoon to create a small cavity.
Allow cookie cups to cool at least 15 minutes to prevent frosting from melting.
Carefully remove cookie cups from the tray using a small spoon or tart tamper to loosen edges.
For the buttercream, beat softened butter, icing sugar, and milk in a stand mixer on medium until smooth, scraping down sides as needed.
Transfer buttercream to a piping bag with your desired tip and pipe into each cookie cup.
Optionally, decorate with sprinkles or festive toppings.