Banana Pudding

3 cups milk
3 large eggs
3/4 cup sugar
1/3 cup all-purpose flour
2 tablespoons butter
2 teaspoons vanilla extract
5 medium-size ripe banana
1 package vanilla wafers
2 cups sweetened whipped cream

1. Whisk together first 4 ingredients in a large saucepan over medium-low heat. Cook, whisking constantly, 15 to 20 minutes or until thickened. Remove from heat; stir in butter and vanilla until butter is melted.
2. Fill a large bowl with ice. Place saucepan in ice, and let stand, stirring occasionally, 30 minutes or until mixture is thoroughly chilled.
3. Meanwhile, cut bananas into 1/4-inch slices. Break cookies into thirds.
4. Spoon half of pudding mixture into a 3-qt. bowl or pitcher. Top with bananas and cookies. Spoon remaining pudding mixture over bananas and cookies. Top with sweetened whipped cream. Cover and chill 2 to 24 hours.