Melt butter in a large nonstick skillet over medium-high heat. Add brown sugar, rum, cinnamon, ginger and 1/4 cup water. Cook, stirring, until sugar dissolves, about 1 minute. Add bananas and sauté until softened, 2 minutes per side. Remove from heat and let cool for 2 to 3 minutes.
Divide ice cream among 4 dessert bowls. Spoon bananas into bowls and drizzle sauce over each. Serve immediately.