Heat the olive oil in a large skillet over medium heat.
Once the oil is hot, add the salmon fillets skin-side down. Cook for 4-5 minutes or until the skin is crispy, then flip and cook for an additional 2-3 minutes. Remove the salmon from the skillet and set it aside.
In the same skillet, add the red curry paste, stirring for about 1 minute until fragrant.
Pour in the coconut milk, fish sauce, and brown sugar. Stir well to combine all the ingredients.
Add the sliced red bell pepper and snap peas to the mixture, stirring occasionally. Cook for about 3-4 minutes until the vegetables are tender yet crisp.
Return the salmon fillets to the skillet, spooning some of the sauce over them. Cover and simmer for 3-5 minutes, until the salmon is cooked through and flakes easily with a fork.
Remove the skillet from the heat, and sprinkle with chopped green onions and fresh basil leaves for garnish.
Serve the coconut red curry salmon over cooked jasmine rice, drizzling with extra sauce as desired.