Skim the coconut cream: Open both cans of coconut milk without shaking them, and carefully spoon off the thick cream that’s risen to the top into a large skillet or wok, setting the remaining thinner liquid aside.
Bloom the curry paste in the cream this is the step that changes everything: Heat the skimmed coconut cream over medium heat until it starts to bubble and separate slightly, then add the red curry paste. Cook, stirring constantly, for 2–3 minutes, until the paste turns a shade darker and smells intensely fragrant rather than raw. Frying the paste in the fat-rich coconut cream instead of dumping it straight into the full can of liquid is what actually unlocks its flavor the chili oils and aromatics in the paste are fat-soluble, so blooming them in hot fat first extracts far more flavor than simmering the paste in liquid ever would.
Add the chicken: Add the sliced chicken to the skillet and stir to coat it in the bloomed paste. Cook for 3–4 minutes, until the outside is no longer pink.
Add the remaining coconut milk: Pour in the reserved thinner coconut milk from both cans and stir to combine. Bring to a gentle simmer.
Add the vegetables and seasonings: Stir in the bell pepper, zucchini, fish sauce, and brown sugar. Simmer for 10–12 minutes, until the chicken is cooked through and the vegetables are tender but not mushy.
Finish with lime and basil: Remove from heat and stir in the lime juice and basil leaves, letting the basil wilt slightly from the residual heat. Pro tip: taste before serving and adjust a little more fish sauce for saltiness, more sugar for sweetness, or more lime for brightness, depending on your curry paste brand’s intensity.
Serve over rice: Spoon the curry over jasmine rice.