Makes 24 cups
Preheat oven to 350 degrees. Brush mini muffin cups lightly with butter.
Lay a sheet of phyllo on a clean work surface and brush with melted butter. Lay another sheet on top and repeat until you have five sheets stacked on top of each other. (Cover the remaining phyllo dough with a damp kitchen towel while it sits on the counter to prevent it from drying out as you work.) Cut stacked phyllo into 3-inch squares and gently press squares down into mini muffin tins. Repeat with remaining phyllo sheets; you should be able to make about 12 cups from each stack for a total of about 24 3-inch squares.
Bake for about 10 minutes, or until golden. (Watch carefully and don't let them burn.) Remove from oven and twist cups out of tins.
Phyllo cups, once cooled, can be stored in a resealable plastic container for up to 3 days.