Warm the oil in a large skillet over medium heat. Add the bell pepper and carrots. Cook for 1-2 minutes, then add the white parts of the chopped green onions and the minced garlic. Cook for another 1-2 minutes, until the veggies are beginning to soften but not yet turn brown.
1 Tablespoon canola oil, 1/2 medium red bell pepper, 1/2 cup shredded carrots, 1/4 cup thinly-sliced green onions, 3 cloves garlic
Stir in the coconut milk, curry paste, fish sauce, and brown sugar. Whisk into a smooth sauce and increase the heat slightly to bring everything to a rapid simmer. Reduce heat to medium-low and let it bubble gently for 3-4 minutes, until slightly thickened.
1 (14 ounce) can unsweetened coconut milk, 2 Tablespoons Thai red curry paste, 2 Tablespoons fish sauce, 2 Tablespoons brown sugar
Keep the sauce at a gentle simmer and add the pieces of chicken. Continue to cook, stirring occasionally, for 5-6 minutes, just until the chicken is cooked through.
1 and 1/4 pounds chicken breasts
Stir in the lime juice, then sprinkle cilantro on top. Sample and season with more lime juice, if desired, or a touch more brown sugar if you want it more sweet.
1 Tablespoon lime juice, 2-3 Tablespoons chopped fresh cilantro
Serve right away over rice or rice noodles, with extra cilantro and the green parts of the chopped green onions on top. Enjoy!