Heat 2 tablespoons butter in a skillet over medium heat. Stir onion, habanero pepper, brown sugar, salt, and pepper into hot butter; cook and stir until onions turn translucent and soften, 5 to 8 minutes.
Stir 1 tablespoon butter into onion mixture and continue to cook and stir until onion caramelizes, 5 to 10 minutes. Remove onions from pan and top with remaining 1 tablespoon butter.