Preheat oven to 425 degrees.
Roast bananas for 10 minutes until a deep brown color on the outside. Take banana flesh out from the skin and add to a blender. Puree flesh until smooth and set aside.
Add the egg yolks and sugar into a bowl. Whisk until a smooth consistency (~1 minute). Set aside.
Add whole milk, heavy cream and vanilla extract to a medium pan. Heat cream until hot and smoke is being emitted from the cream. Turn off the heat.
Add 1/4 cup of the hot cream to the eggs and whisk until it turns a smooth and uniform yellow color. The goal of this step is to raise the temperature of the eggs, so they don’t completely cook in the hot cream. Pour the eggs into the pan with the hot cream.
Turn the heat back on and heat the cream until it reaches 170 degrees F. A good way to test if it’s done is to coat the back of a spoon with the cream and pull your finger through the cream. A done cream should have a thick, smooth trail that doesn’t break. Take the cream off the heat.
Add the pureed bananas to the cream and blend using an immersion blender or in a regular blender. Pulse only a few times until the bananas and cream are well combined. Be careful not to over mix.
Cool the cream down to room temperature and then put it in the fridge to cool completely. The cream should be in the fridge for about 6-8 hours. This will help create a creamier texture.
Pour the cream into an ice cream maker and churn for 10-15 minutes.
When there are about 3 minutes left in churning time, melt your chocolate. Add chocolate chips to a microwave safe bowl and heat in 30 second increments in the microwave. Make sure to stir the chocolate in between each increment. It should take about 1-2 minutes for the chocolate to melt completely. Add the melted chocolate to a liquid measuring cup.
When there are 30 seconds left in churning time, stream the melted chocolate into the churning ice cream. The cold ice cream will harden the chocolate, so you get chocolate streaks throughout the ice cream.
Spoon the ice cream into an ice cream container. Freeze overnight and serve!