Preheat the oven to 350°F and lightly grease a standard loaf pan
Finely shred the zucchini. If it is very watery, gently squeeze out some excess moisture
Whisk together the flour, cocoa powder, baking soda, baking powder, salt, and cinnamon
In a separate bowl, whisk the egg, sugar, oil, and vanilla. Stir in the shredded zucchini
Add the dry ingredients to the wet ingredients and mix just until combined. Fold in the chocolate chips
Transfer the batter to the prepared loaf pan and bake for 45 to 55 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs
Cool the bread completely before cutting it into small pieces
Beat the cold heavy cream with an electric mixer until stiff peaks form
In a separate bowl, stir together the sweetened condensed milk, vanilla, and salt.
Gently fold the condensed milk mixture into the whipped cream.
Fold in the chopped chocolate zucchini bread and chocolate chips.
Transfer the mixture to a parchment-lined loaf pan or freezer-safe container. Add extra bread pieces and chocolate chips between layers if desired
Cover tightly and freeze for at least 6 hours, preferably overnight
Let the ice cream sit at room temperature for 5 to 10 minutes before scooping.