In a large 12-inch stainless-steel skillet over medium-high heat, melt butter with the brown sugar, cinnamon, nutmeg, and salt while stirring and swirling, until mixture blends into a grainy liquid and begins to bubble, about 2 minutes. Add bananas, cut side down, and continue to cook, swirling gently, until liquid begins to resemble a more smooth caramel, about 2 minutes longer.

Add rum (do not pour directly from the bottle if working over an open flame), then tilt pan to ignite the alcohol from a gas burner, or carefully light with a match. Cook, shaking the pan, until the flames have died out and the caramel has thickened to a honey consistency, about 1 to 2 minutes. Alternatively, you can add the rum and not light it on fire, instead simmering until the rum has mostly cooked off and the caramel has reached a honey consistency.

Flip bananas cut side up, then transfer to serving plates with ice cream (2 pieces of banana each for 6 servings; 3 pieces of banana each for 4 servings; 4 pieces of banana each for 3 servings; or 6 pieces of banana each for 2 servings, if you're as gluttonous as I was on the day we photographed this).