Combine first 3 ingredients in a heavy saucepan; whisk in eggs and milk, and cook, whisking constantly, over low heat until thickened (about 25 minutes.) Remove from heat and stir in butter and vanilla. Set custard aside.
Spread a 1/2 teaspoon of peanut butter between 2 chocolate wafers, forming a sandwich; repeat with remaining peanut butter and chocolate wafers.
Place sandwich cookies in the bottom of a 3-quart glass bowl or trifle bowl; top with banana slices. Pour custard over bananas. Cover and chill 4 hours.
Spread whipped topping evenly over the custard and sprinkle with peanuts before serving.