1. Preheat oven to 350°. Beat first 4 ingredients with an electric mixer at medium speed until blended. Add egg; beat well.
2. Combine flour and next 3 ingredients; add to butter mixture, blending well. Shape dough into 1-inch balls on ungreased baking sheets. Gently flatten with a fork dipped in sugar, making a crisscross pattern on each. Bake 8 minutes. Remove to wire racks to cool.
3. Combine ice cream and banana until well blended. Scoop 1 rounded tablespoon ice cream onto 1 cookie, and top with another cookie, pressing lightly to make a sandwich. Freeze 45 minutes or until firm.