Place 1 cup of ice cream in each of 4 decorative glasses or bowls. Set the glasses in the freezer.
Melt the butter in a skillet over medium-high heat. Stir in the brown sugar and cook until dissolved into the butter. Whisk in the orange and lime juice and simmer until a smooth sauce forms. Mix in the spices. Add the nectarines and cook, turning once, for 2 minutes. Add the rum, tilt the pan slightly, and very carefully ignite with a long match. Cook, swirling the pan, until the flames die out. Divide and set the nectarine wedges in the ice cream filled glasses. Spoon over the sauce, garnish with mint, and serve immediately.