Heat oven to 350°F. Break apart cookie dough; press into ungreased 15x10x1-inch pan. Bake 14 to 18 minutes or until golden brown. Cool completely, about 30 minutes. Line 8-inch springform pan with heavy-duty foil, leaving ends hanging over.
Crumble baked cookie into large resealable food-storage plastic bag. Using rolling pin, crush cookie to fine crumbs. Reserve 1/4 cup of the crumbs. Evenly spread one-third of remaining cookie crumbs (about 1 cup) into bottom of springform pan.
Meanwhile, in medium bowl, stir together half of the vanilla ice cream (about 1 3/4 cups) and the blueberries. Spread in pan.
Top with 1 cup of the cookie crumbs. Cover loosely with a layer of foil; freeze about 30 minutes or until firm.
Remove foil. Spread softened sorbet evenly over cookie crumbs. Top with remaining cookie crumbs (about 1 cup). Cover loosely with a layer of foil; freeze about 30 minutes or until firm.
In large bowl, stir together remaining vanilla ice cream (about 1 3/4 cups) and the strawberries. Remove foil. Spread in pan. Cover pan with foil; freeze 8 hours.
Sprinkle with reserved cookie crumbs. Remove side of pan, and use foil as handles to lift cake off pan base. Remove foil. Place ice cream cake on serving plate. Store covered in freezer.