In a large skillet or wok, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until it becomes translucent. Then, add the minced garlic and cook for an additional minute until fragrant.
Stir in the Thai red curry paste, mixing it well with the onions and garlic. Allow it to cook for about 2 minutes, which will help release its aromatic flavors.
Add the chicken broth and fish sauce to the skillet, stirring to combine. Next, pour in the full-fat coconut milk, mixing everything together until the curry base is smooth and creamy.
Add the chopped red bell pepper to the skillet and bring the mixture to a gentle simmer. Let it cook for about 5 minutes, allowing the flavors to meld and the bell pepper to soften slightly.
Add the thawed shrimp to the skillet, stirring gently to coat them in the sauce. Cook for about 3-4 minutes, or until the shrimp turn pink and opaque. Be careful not to overcook them, as they can become tough.
Once the shrimp are cooked, squeeze fresh lime juice over the curry to brighten the flavors. Season with salt and pepper to taste. Finally, stir in the chopped cilantro and basil just before serving.