Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large bowl, beat butter, granulated sugar, and powdered sugar until light and fluffy.
Add eggs one at a time, then mix in vanilla extract.
In another bowl, whisk together flour, baking powder, and salt. Gradually mix into the wet ingredients.
Divide dough into three equal portions. Tint each with a different gel food coloring (purple, pink, blue).
Take small pieces of each color and press them together, forming a marbled dough. Roll out to 1/4-inch thickness.
Use a round cutter to cut out cookies. Decorate with sprinkles and place on baking sheet.
Bake for 8–10 minutes or until edges are set. Let cool completely.
Scoop softened ice cream onto the flat side of a cookie, top with another cookie, and gently press to form a sandwich.
Freeze sandwiches for at least 2 hours before serving.