Heat the oil in a large pot over medium-high heat. Add the onion and pepper and sauté until tender, 4 to 5 minutes.
Add the garlic and ginger and cook until fragrant, a minute or so longer.
Stir in the curry paste, and then add the broth, coconut milk, and chicken. Simmer 10 minutes to blend the flavors.
Stir in the lime juice and cilantro. Taste and adjust the seasonings.
Serve with lime wedges over a cup of cooked basmati rice. If you’ve got fresh basil around, toss it in along with the cilantro.