Pat the salmon fillets dry with paper towels and season both sides with salt and pepper.
Heat a large skillet over medium-high heat and add 2 tablespoons of butter, allowing it to melt.
Carefully add the salmon fillets to the skillet, skin-side down if applicable, and cook for 4-5 minutes without moving them to achieve a nice sear.
In a small bowl, prepare the garlic butter by mixing the remaining 2 tablespoons of butter, minced garlic, lemon juice, and chopped parsley.
Flip the salmon fillets gently with a spatula and cook for another 3-4 minutes, or until the salmon flakes easily with a fork.
In the last 2 minutes of cooking, spoon the garlic butter mixture over the salmon, allowing it to melt and baste the fillets.
Once cooked through, remove the salmon from the skillet and place it on a serving platter. Drizzle any remaining garlic butter sauce from the skillet over the top and serve with lemon wedges.
For an optional kick, consider adding a pinch of red pepper flakes to the garlic butter sauce before serving.