Start by heating a large skillet over medium heat. Add 2 tablespoons of the butter and allow it to melt.
Once the butter is melted, season the salmon fillets with salt and black pepper on both sides. Place the salmon in the skillet, skin-side down, and cook for about 4-5 minutes until the skin is crispy and the fish is nearly cooked through. Flip the salmon fillets and cook for an additional 2-3 minutes. Remove the salmon from the skillet and set aside on a plate.
In the same skillet, add the remaining 2 tablespoons of butter. Add the minced garlic and sauté for about 30 seconds until fragrant.
Add the sliced mushrooms to the pan and cook for about 4-5 minutes, until softened.
Stir in the fresh spinach and cook until wilted.
Reduce the heat to low and pour in the heavy cream. Add the Dijon mustard, and season with salt and black pepper to taste. Whisk the sauce to combine and let it simmer for about 2-3 minutes until slightly thickened.
Return the salmon fillets to the skillet, spooning the creamy sauce over the top. Cook for an additional 2 minutes just to warm the salmon through.
Drizzle the lemon juice over the dish before serving. Garnish with fresh parsley if desired.