Mash bananas to rough texture. Cover and set aside.

Place 1/2 cup of sugar and lemon juice in 2 1/2 quart saucepan. Stir to combine (sugar will look like moist sand). Caramelize the sugar for 5-6 minutes over medium high heat, stirring with whisk constantly. Reduce heat to low.

Carefully and slowly add the heavy cream, then the half and half into the sugar. It will steam and boil rapidly. Add 1/2 cup of sugar and whisk to dissolve. Bring to a boil, about 5 minutes.

While heating the cream, place the egg yolks and the remaining 1/2 cup sugar in a Mix Master and beat with a paddle on high for 2 1/2 minutes. Scrape the sides of bowl then beat until lemon-colored, about 3 minutes more.

Pour boiling caramel cream into the beaten egg yolks (I temper carefully) and whisk to combine. Return to the saucepan and heat over medium-high, stirring constantly, until it comes to a temperature of 185 degrees, about 2-4 minutes. Remove from heat, pour over the smashed bananas, and put in an ice water bath until it drops to 40-45 degrees, about 15 minutes.

Once cold, fold in chocolate chips and freeze in ice cream maker according to manufacturer's instructions.

Makes 2 quarts.