Sear the haddock: Heat the olive oil or butter in a large skillet over medium-high heat. Season the haddock fillets with salt and pepper, and sear them for 3-4 minutes on each side until golden brown and cooked through. Remove the fish from the skillet and set aside.

Sauté the garlic: In the same skillet, lower the heat to medium and add the minced garlic. Sauté for 1-2 minutes until fragrant, being careful not to burn the garlic.

Make the cream sauce: Stir in the chicken or fish broth, scraping up any browned bits from the bottom of the skillet. Let it simmer for 3-4 minutes. Stir in the heavy cream and Dijon mustard (if using). Let the sauce simmer for another 3-5 minutes until it thickens slightly.

Add the Parmesan and finish: Stir in the Parmesan cheese and fresh parsley. Let the sauce simmer for 1-2 more minutes until it becomes creamy and smooth. Season with salt and pepper to taste.

Serve: Return the haddock fillets to the skillet and spoon the garlic cream sauce over the fish. Serve hot, garnished with fresh parsley and lemon wedges for extra brightness.