Heat the vegetable oil in a large pot over medium heat. Add the onion and red bell pepper and cook for 3 to 4 minutes until they begin to soften.
Stir in the garlic and ginger and cook for 1 minute until fragrant.
Add the Thai red curry paste and stir for 30 seconds to toast it lightly.
Pour in the coconut milk, then add the fish sauce and brown sugar. Stir well and bring the mixture to a gentle simmer.
Add the shrimp and cook for 4 to 5 minutes until they turn pink and opaque.
Remove the pot from the heat and stir in the lime juice.
Spoon the curry over cooked rice and top with chopped cilantro before serving.