Pat chicken pieces dry and season lightly with salt and pepper.
Heat oil in a large skillet or wok over medium-high heat.
Add chicken in a single layer and brown for 3–4 minutes per side until just cooked; remove and set aside.
Lower heat to medium, add a splash of oil if needed, then sauté sliced onion until translucent.
Stir in garlic and grated ginger; cook 30–45 seconds until fragrant.
Add curry paste and toast briefly, stirring to coat the aromatics.
Pour in coconut milk and chicken broth, whisking to blend with the paste.
Stir in fish sauce and brown sugar; bring sauce to a gentle simmer.
Return chicken to the pan and add sliced bell peppers; simmer 6–8 minutes until chicken is cooked through and peppers are tender-crisp.
Squeeze in lime juice, adjust seasoning with salt, pepper, or a little extra fish sauce, garnish with cilantro and serve hot over rice or noodles.