1. Season both sides of the salmon with salt and black pepper.

2. Heat the olive oil in a large skillet over medium-high heat. Add the salmon and sear for about 4 minutes per side, or until golden and cooked to your liking. Transfer the salmon to a plate.

3. Carefully remove excess oil from the skillet, leaving a small amount behind. Add the butter and let it melt, then stir in the garlic. Cook for about 30 seconds, just until fragrant.

4. Lower the heat to medium-low. Pour in the chicken broth and heavy cream, stirring to combine.

5. Add the Parmesan cheese and stir until melted into a smooth sauce. Season with parsley, salt, and pepper.

6. Simmer for 2 to 3 minutes, until the sauce slightly thickens. Return the salmon to the skillet and spoon the sauce over the top. Cook for another 1 to 2 minutes, until warmed through.

7. Serve hot with extra parsley and a squeeze of lemon juice, if desired.