Preheat the oven to 375°F. Combine cookie mix, butter, and egg in a large bowl and mix with a spoon until a soft dough forms. Shape the dough into 36 (1 1/4-inch) balls (approximately 1 tablespoon each) and place them in ungreased mini muffin cups. Press an indentation in the center of each ball using the end of a wooden spoon.
Bake until edges are light golden brown, about 8 to 10 minutes. Use the end of a wooden spoon to make a 1-inch indentation in the center of each cookie while they are still warm, cleaning the end with a paper towel as needed. Let the cookies cool in the pan for 15 minutes, then transfer to a cooling rack to cool completely.
Fill a resealable plastic bag with frosting and cut off a corner. Pipe frosting into the center of each cookie cup, using about 1 teaspoon for each. Cut truffles in half with a small serrated knife and place a half on top of the frosting in each cup. Drizzle with cookie icing and sprinkle with candy sprinkles.