To make the paçoca ice cream wrap the ice cream bowl/bucket in plastic wrap (in order to keep it clean) and freeze it for about 24 hours prior to making the ice cream.
Heat a large, non-stick frying pan over medium-high heat and melt the butter. Reduce heat to medium and cook the quartered bananas (chunks) for about 1 minute, tossing the bananas by shaking the pan around occasionally. In a small bowl, mix together 1/4 cup sugar and 1 teaspoon cinnamon. Pour on top of the bananas and let cook for about 2 minutes, shaking the pan occasionally. Remove from heat and drizzle the lime juice on top of the bananas, swirling the pan in a circular motion to coat them. Transfer to a bowl, let cool, and freeze. Meanwhile, in a large bowl, whisk together the ground paçoca, heavy cream, condensed milk, remaining 1/4 cup sugar and 1/8 teaspoon cinnamon, vanilla, and salt until smooth.
If using an ice cream machine: Pour the cream mixture into the ice cream machine frozen bowl/bucket, and follow the manufacturer’s instructions. Churn for 25 to 30 minutes or until firm. Transfer the ice cream to a container, fold in the frozen bananas chunks, cover (with a lid or plastic wrap), and store in the freezer for at least 24 hours. Serve by itself or with fried bananas on top drizzled with chocolate sauce.
If NOT using an ice cream machine: Follow the instructions above for preparing the banana chunks and also the ice cream mixture. Transfer the ice cream mixture to an airtight container and cover with plastic wrap. After the ice cream has been in the freezer for 60 to 90 minutes, remove from the freezer and stir vigorously with a wooden spoon or plastic spatula. Freeze ice cream again and continue to stir every 30 minutes for 2 to 3 hours. Fold in the frozen bananas chunks, cover (with a lid or heavy duty aluminum foil), and store in the freezer for at least 24 hours. Serve by itself or with fried bananas on top drizzled with chocolate sauce.
For the fried bananas, heat a large, nonstick frying pan over medium-high heat and melt the butter. Reduce heat to medium and cook the banana for about 1 minute, shaking the pan occasionally. In a small bowl, mix together the sugar and cinnamon. Pour over the bananas and let cook for 2 to 3 minutes, shaking the pan occasionally. Remove pan from the heat and let cool a little bit before serving on top of the ice cream with the chocolate sauce.
For the chocolate sauce, place the chocolate chips and heavy cream in a medium microwave-safe bowl and heat at medium power (50%) for 1 to 1-1/2 minutes. Stir well, heating at 15 to 30 seconds intervals if necessary, stirring until smooth. Drizzle on top of the fried bananas.