Heat oil in a large pot or Dutch oven over medium-high; cook onion 3-4 minutes until softened.
Add garlic and ginger; cook 1 minute until fragrant. Stir in curry paste; cook 2 minutes, stirring constantly to bloom spices.
Stir in coconut milk and broth to combine with paste; mix in fish sauce and sugar well.
Add potatoes and carrots; simmer 10 minutes until vegetables start softening.
Add chicken and pepper; simmer 12-15 minutes until chicken is cooked through and vegetables tender, stirring occasionally.
Remove from heat; stir in lime juice. Taste; add fish sauce if needed.
Serve over jasmine rice, garnished with basil.