Begin by patting the salmon fillets dry with paper towels. Season both sides generously with sea salt and allow them to sit at room temperature for about 15 minutes.
Place your skillet over medium-high heat and add the olive oil. Allow the oil to heat until it shimmers.
Once the oil is hot, carefully place the salmon fillets skin-side down in the skillet. Cook for about 5-7 minutes without moving them.
Carefully flip the salmon fillets over, add the butter to the pan, and let it melt, spooning it over the salmon as it cooks for another 3-4 minutes.
Check the salmon for doneness; it should flake easily with a fork and have an internal temperature of 125°F to 130°F for medium-rare.
Remove the salmon from the skillet, squeeze fresh lemon juice over the top, and sprinkle with fresh herbs if desired. Serve immediately.