Remove the salmon from the fridge and allow it to sit at room temperature for 15–20 minutes. Cut the fillet into four equal portions and pat each piece dry. Season both sides with salt and pepper.

Place a large skillet over medium-high heat and add 1 tablespoon of olive oil and 1 tablespoon of butter. Once the butter melts and begins to sizzle, add the salmon skin-side down and cook for about 5 minutes.

Carefully flip the salmon pieces and cook for an additional 2-4 minutes until the flesh is opaque and flakes easily. Transfer the salmon to a plate and cover loosely with aluminum foil.

Reduce the heat to medium, add 2 tablespoons of butter to the same skillet, then add 2-3 cloves of minced garlic. Cook for about 1 minute until fragrant but not burnt.

Squeeze half a lemon into the skillet, whisking it into the melted butter. Cook for an additional 30 seconds.

Return the salmon to the skillet, spoon the sauce over each piece, and warm for a minute. Garnish with parsley and serve immediately with lemon wedges.