In a large skillet, stir together brown sugar, butter, vanilla, salt, and cinnamon; cook over medium-high heat, stirring frequently, until butter is melted and mixture is bubbly. Add bananas, cut side down; reduce heat to medium, and cook until bananas are lightly golden, 1½ to 2 minutes per side. Remove from heat; add rum to pan. Using a stick lighter or candle lighter, carefully light sauce. (See Note.) Stir and spoon flaming sauce over bananas until flame is extinguished. Sprinkle with pecans, and serve with vanilla ice cream.