Step 1In a non-stick skillet over medium-high heat, combine the sugar and oil, stirring frequently until the sugar is melted. Add the pecans and stir to coat completely. Remove from heat and spread the nuts out on a greased sheet of parchment paper to cool.
Step 1In the bowl of a food processor, grind the nuts until they are reduced to a coarse meal, 2 to 3 minutes. Add the oil and sugar and continue to process until the nuts are reduced to a smooth paste, 3 to 4 minutes, scraping down the bowl as needed.
Step 2Add the bananas and continue to process until the mixture is smooth and creamy, about 3 minutes, scraping down the bowl as needed. Add the cinnamon, vanilla and rum if using, and pulse a few times to combine. Stir in the candied pecans by hand.
Step 3Spoon the ice cream into a glass or plastic dish and cover the surface of the ice cream with plastic wrap before freezing.