Stir eggs and sugar together in a saucepan, blend well. Add cornstarch, salt, and milk. Cook on stovetop using medium-high heat, stirring constantly (about 10-12 minutes) until pudding is thick. Remove from heat and add your vanilla extract and bananas. Stir well. Pour pudding into a glass bowl and cover with plastic wrap. Cool in refridgerator or serve warm. Enjoy!