Pour off all but 1 teaspoon oil from pan used to cook chops and return pan to medium heat. Add shallot, garlic, and ginger and cook, stirring constantly, until softened, about 1 minute. Add broth, coconut milk, and sugar, scraping pan bottom to loosen browned bits. Simmer until reduced to 1/2 cup, 6 to 7 minutes. Off heat, stir in cilantro and lime juice, then whisk in butter. Season with salt and pepper and serve with chops.

Makes 1/2 cup