Equipment: Measuring cup, measuring spoons, 2 stainless steel bowls (1 large), slotted spoon, film wrap, 2 1/2-qt saucepan, whisk, electric mixer with paddle, rubber spatula, instant-read test thermometer, ice-cream freezer, 2-qt plastic container with lid

Peel the bananas. Using a slotted spoon, smash them to a rough-textured consistency in a stainless steel bowl. Cover with film wrap and set aside.

Place 1/2 cup of sugar and the lemon juice in a 2 1/2-qt saucepan. Stir with a whisk to combine (the sugar will resemble moist sand). Caramelize the sugar for 5 to 6 minutes over medium-high heat, stirring constantly with a whisk to break up any lumps (the sugar will first turn clear as it liquefies, then light brown as it caramelizes). Reduce the heat to medium.

Carefully and slowly pour the heavy cream, then the half-and-half into the caramelized sugar (the mixture will steam and boil rapidly as the cream is added). Add 1/2 cup of sugar and whisk to dissolve. Bring to a boil, about 5 minutes.

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