Heat the vegetable oil in a large pan or wok over medium heat.
Add the red curry paste to the pan and stir-fry for 1-2 minutes to release its flavors.
Pour in the coconut milk and chicken or vegetable broth. Stir well to combine.
Add the shrimp, bell pepper, and onion to the pan. Cook for 5-7 minutes until the shrimp are pink and cooked through.
Stir in the fish sauce and brown sugar. Adjust the seasoning according to your taste preferences.
Remove from heat and garnish with fresh basil leaves.
Serve the Thai Red Curry with Shrimp over steamed rice.