Heat vegetable oil in a large pot or Dutch oven over medium-high heat. Add diced onion and cook for 3-4 minutes until softened.
Add garlic and ginger, cooking for 1 minute until fragrant. Stir in yellow curry paste and cook for 2 minutes, stirring constantly to bloom the spices.
Pour in coconut milk and chicken broth, stirring to combine with the curry paste. Add fish sauce and brown sugar, mixing well.
Add cubed potatoes and sliced carrots to the pot. Bring to a simmer and cook for 10 minutes until vegetables begin to soften.
Add chicken pieces and bell pepper strips to the curry. Simmer for 12-15 minutes, stirring occasionally, until chicken is cooked through and vegetables are tender.
Remove from heat and stir in fresh lime juice. Taste and adjust seasoning with additional fish sauce if needed.
Serve curry over jasmine rice, garnished with fresh basil leaves.