Season thighs with salt and pepper. Brown in oil over medium-high heat, 4–5 minutes per side; set aside.
Sauté onion until soft, add garlic and ginger, cook 1 minute. Stir in curry paste and toast briefly.
Pour in coconut milk and broth, whisk to combine. Add fish sauce, sugar, and return thighs to pan.
Simmer, covered, 25–30 minutes until chicken is tender and cooked through.
Add bell pepper and snap peas in last 5 minutes to keep them crisp.
Stir in basil and lime juice just before serving. Adjust seasoning.