Pat the salmon fillets dry with paper towels and season on both sides with salt and pepper. In a 12-inch/30 cm skillet, heat 1 tablespoon olive oil over medium-high. Add the salmon fillets and sear, skin side down if applicable, without moving them, until deeply golden on the bottom, about 3 to 4 minutes. Flip and sear the second side for 2 minutes. Transfer to a plate; the salmon will finish cooking in the sauce.

Lower the heat to medium and add the remaining tablespoon of olive oil. Stir in the sliced red pepper and cook for 2 to 3 minutes, just until beginning to soften. Add the garlic and ginger and sauté until fragrant, about 1 minute.

Add the red curry paste and cook, stirring constantly, for 30 seconds to bloom the spices. Pour in the coconut milk and stir in the soy sauce or fish sauce, sugar, and chickpeas. Bring to a gentle simmer, scraping up any bits stuck to the bottom of the pan.

Return the salmon to the pan and reduce the heat to low. Simmer uncovered for 5 to 8 minutes, spooning sauce over the fillets occasionally, until the salmon is just cooked through and flakes easily with a fork.

Remove from heat and squeeze lime juice over the curry. Garnish with lime slices and chopped cilantro. Serve warm with jasmine rice, basmati rice, or warm naan.