Prepare the Salmon: Season the salmon fillets with salt and pepper on both sides.
Sear the Salmon: In a large skillet, heat the olive oil over medium-high heat. Once hot, carefully place the salmon fillets skin-side down in the skillet. Cook for about 4-5 minutes until the skin is crispy, then flip and cook for an additional 3-4 minutes until the salmon is cooked through. Remove the salmon from the skillet and set aside.
Make the Creamy Sauce: In the same skillet, reduce the heat to medium and add the minced garlic. Sauté until fragrant, about 30 seconds.
Add Liquid Ingredients: Pour in the chicken broth, stirring to scrape up any bits from the bottom of the skillet. Let it simmer for 1-2 minutes. Then, stir in the heavy cream, Dijon mustard, lemon zest, and lemon juice. Allow the mixture to simmer for about 3-5 minutes until it slightly thickens.
Combine: Gently place the cooked salmon back into the skillet with the creamy sauce. Spoon some of the sauce over the salmon and let it simmer for another minute to heat through.
Finish and Serve: Remove from heat and sprinkle with fresh parsley. Serve the salmon with lemon wedges on the side and drizzle with extra creamy sauce.