Pat the salmon fillets dry and season both sides with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Sear the salmon for 3-4 minutes per side until golden brown and crusty; remove salmon from the skillet and set aside on a plate.
Reduce heat to medium. Add butter to the skillet and melt until bubbling. Add shallots, garlic, and ginger, sautéing for 2 minutes until translucent and fragrant.
Incorporate the red curry paste into the aromatics, stirring constantly for 1 minute to toast the spices.
Pour in the coconut milk and bring to a gentle simmer. Use a wooden spoon to deglaze the pan by scraping up the browned bits (fond) from the bottom.
Simmer the sauce for 5 minutes until slightly thickened. Stir in the lime juice and baby spinach, cooking until the spinach has wilted.
Place the salmon fillets back into the skillet. Spoon the curry sauce over the fish and cook for an additional 2 minutes to warm through.
Garnish with fresh cilantro and serve over rice or cauliflower rice.