Heat oven to 375° F. Spread the pecans on a rimmed baking sheet and toast, tossing occasionally, until fragrant, 5 to 6 minutes; roughly chop.

Melt the butter in a large skillet over medium-high heat. Add the sugar and cinnamon and cook, whisking occasionally, until smooth, 4 to 5 minutes.

Gently stir in the bananas. Remove from heat and add the rum. Using a match, carefully ignite the mixture and wait until the flame goes out. Stir in the pecans.

Serve the bananas and sauce over the ice cream.