Pat the salmon fillets dry with a paper towel. Season both sides evenly with 1/4 tsp sea salt, 1 tsp ground paprika, and 2 tsp dried dill.
Heat 1 to 2 Tbsp avocado oil in a large cast-iron or nonstick skillet over medium-high heat until the oil is hot.
Place the salmon fillets flesh side down in the skillet, pressing lightly so the flesh makes full contact with the pan. Sear undisturbed for 3–4 minutes, until the surface is crispy and golden.
Flip the salmon and sear the other side for 2–3 minutes.
Flip the salmon again and cook another 1–2 minutes.
Add 1 cup full-fat canned coconut milk, 2 tsp lemon zest, 2 Tbsp lemon juice (to taste), 3 Tbsp capers, and the remaining 2 tsp dried dill to the skillet. Reduce heat to medium-low and cook, spooning the sauce over the fillets, until the sauce thickens and the salmon reaches your desired doneness, about 3–4 minutes.
Taste the sauce and add additional sea salt and/or more lemon juice if needed.
Check the salmon’s internal temperature with a meat thermometer: the FDA considers salmon fully cooked at 145°F; medium-rare is about 120–125°F. Remove from heat when it reaches your preferred temperature and serve.