Prep the salmon by taking it out of the refrigerator 30 minutes before cooking so it can come to room temperature. If needed, slice the salmon into two same-sized pieces, then pat them very dry with paper towels to soak up moisture from both sides of the filets. Season both sides with sea salt and freshly cracked black pepper, to taste.
Sear the salmon by heating the olive oil in a large skillet (or cast iron skillet) over medium-high heat. Once hot, add salmon, skin side up, and cook for 2 1/2-3 minutes until golden.
Carefully flip the salmon filets over and cook for 1 minute.
Baste the salmon by adding the butter and cooking for 30 seconds until melted and bubbling. Add the garlic, then tilt the skillet slightly and start spooning the garlic butter continuously over the salmon for 1 minute or until it reaches an internal temperature of 122 degrees for medium-rare.
Rest the salmon by immediately removing the filets to a serving plate. Rest for 3 minutes, the temperature will rise to around 127-130 degrees with a meat thermometer.
Place the skillet back on the stove over medium-high heat, add the lemon juice to the garlic butter, and add the parsley; whisk until well combined.
Serve salmon with lemon garlic butter sauce spooned over the salmon, along with some lemon wedges.