Heat oven to 350°F. Spray cookie sheet or 12-inch pizza pan with cooking spray. In medium bowl, break up cookie dough; mix in ginger and cinnamon. Knead dough with hands until well mixed. With floured fingers, pat dough into 12-inch round on cookie sheet.
Bake 18 to 20 minutes or until golden brown. Cool completely on cooling rack, about 30 minutes.
Spread ice cream over baked crust. Spread with whipped topping. Sprinkle with gingersnaps and toffee bits. Freeze until ice cream is firm, at least 1 hour. Cut into wedges.