In a medium saucepan, whisk the eggs until smooth. Stir in the flour and sugar.

Slowly add milk while stirring. Cook over low heat, stirring constantly, until the mixture thickens into a pudding-like consistency.

Remove from heat and stir in the butter and vanilla. Mash the bananas and mix them into the pudding.

Divide the pudding into four small mason jars or serving cups.

Chill for at least 1 hour. Before serving, garnish with banana slices or crushed vanilla wafer crumbs if desired.