Heat the oil in a large pot over medium heat. Add the onion and 1 teaspoon of the salt, and sauté until it starts to soften.
Stir in the garlic, ginger, and curry paste and sauté for another minute, until fragrant.
Pour in the coconut milk and brown sugar.
Add the chicken, bell peppers, zucchini, and carrots to the pot along with remaining teaspoon of salt.
Bring the curry to a simmer, then reduce the heat to low. Let it cook uncovered for about 15 minutes, until the chicken is cooked through and the vegetables are tender.
Sprinkle on the fresh basil leaves just before serving. Serve with lime wedges if desired.