In a large bowl, mash bananas well, add egg, and mix together. Add yeast, salt, dried fruit, and melted butter, mixing well to combine. Add flour in two batches, mixing with a spatula or paddle until all flour has been incorporated and the dough is sticky. Scrape sides of bowl, placing the dough in a round shape in the center. Cover and let rise for 1½ hours, or until doubled in size.
Drop onto a lightly floured surface and work into a cylinder shape. Cut into 9 equal pieces. Tuck the bottom of each piece into the middle and roll into a tight ball. Place rolls into 10 x 10-inch baking dish greased with butter so the rolls are touching. Cover and proof for another 1½ hours, or until doubled in size. Uncover and brush with melted butter.
Preheat oven to 350 F and bake for 20 to 25 minutes. Let cool to the touch, then tear apart and serve. Store in an airtight container for up to 3 days. Eat for breakfast, a snack, or a sweet dinner roll.
Per serving: 275 calories, 11 grams fat (7 grams saturated fat), 48 milligrams cholesterol, 210 milligrams sodium, 40 grams total carbohydrates, 2.5 grams fiber, 5 grams protein.
