In a large mixing bowl, combine gingerbread mix, melted butter, and egg. Add up to 1/4 cup flour if dough seems too wet.
On a lightly floured surface, roll out dough to 1/4-inch thickness. Cut out dough with a 2-inch round cookie cutter and transfer to an ungreased cookie sheet. Bake for 10 minutes. Cool completely on a cooling rack.
Sprinkle the cinnamon into the ice cream. Spread ice cream on bottom half of cooled cookies and top with remaining cookies. Dip sandwiches in sprinkles for fun.