Step 1

Melt 2 tablespoons of the butter in a medium skillet over medium; stir in 1⁄4 cup of the brown sugar until combined. Stir in bananas and 1⁄2 tablespoon of the rum; cook, stirring often, until bananas soften and begin to break down, 3 to 4 minutes. Set aside; let cool completely, about 20 minutes.

Step 2

Preheat oven to 375°F. Stir together cinnamon, 1⁄4 cup of the brown sugar, and 2 tablespoons of the granulated sugar in a small bowl. Unroll 1 can of crescent roll dough on a lightly floured surface. Separate dough piece along center perforation to form 2 (7 1⁄2- x 6-inch) rectangles; press perforations to seal. Repeat with remaining can.

Step 3

Spread the 4 dough rectangles evenly with the softened butter, and sprinkle each with about 2 tablespoons of the cinnamon-sugar mixture. Dollop each rectangle with one-fourth of cooled banana mixture, and carefully spread a thin layer of the mixture to within 1⁄4 inch of edges. Roll up each rectangle, jelly-roll fashion, starting at long end.

Step 4

Gently cut each dough log into 6 even slices, using a serrated knife. Place rolls in 2 (12-cup) mini muffin pans lined with miniature paper baking cups. Bake in pre-heated oven until golden brown, 14 to 16 minutes. Let cool on wire racks 15 minutes.

Step 5

Place cream, salt, and remaining 1⁄4 cup each butter, brown sugar, and granulated sugar in a small saucepan over medium. Bring to a boil, whisking constantly; boil 1 minute. Remove from heat, and whisk in remaining 1 tablespoon rum. Gradually whisk in 1⁄2 cup of the powdered sugar until smooth. Whisk in remaining 1 to 3 tablespoons powdered sugar, 1 tablespoon at a time, until desired consistency is reached. Drizzle slightly warm buns with glaze, and sprinkle with toasted pecans.