Cracker Barrel Old Country Store Banana Pudding

Source: Cracker Barrel Restaurant - Phoenix, Arizona

1 1/2 quarts milk
1 1/4 cups liquid eggs
1/4 cup imitation vanilla extract
1 1/8 cups flour
1 1/4 cups granulated sugar
12 ounces Nilla Wafers
1 3/4 bananas, peeled
8 ounces Cool Whip