Preheat your oven to 400°F (200°C). Lightly grease a baking dish with olive oil.
Pat the salmon dry with paper towels. Season both sides generously with salt and black pepper.
Heat olive oil in a skillet over medium-high heat. Sear the salmon fillets for 2 minutes on each side until golden. Transfer them to the baking dish.
In the same skillet, melt butter. Add garlic and sauté until fragrant.
Pour in the chicken broth, lemon juice, and heavy cream. Stir well and let simmer for 2–3 minutes until the sauce thickens slightly. Add lemon zest and parsley.
Pour the sauce over the salmon in the baking dish.
Bake uncovered for 12–15 minutes, until the salmon flakes easily with a fork.
Serve hot, garnished with lemon slices and extra parsley if you like.