Pat the fillets dry with paper towels. Season with salt and black pepper on both sides of fillets.
Heat the oil in a skillet over medium-high heat. Gently place the salmon fillets (flesh side down) in a pan. Cook, undisturbed for 3 minutes or until golden brown. Flip the fillets, cook the skin until it's crispy and the fish is cooked to your liking (see notes). Transfer them to a plate.
In the same skillet, melt butter then saute shallots for 1 minute. Add the garlic, then saute until fragrant.
Add the wine and gently scrape the brown bits from the bottom of the pan with a spatula. Bring to simmer over medium-high heat until it reduces to about 1-2 tablespoons, then add Dijon mustard and stir for a few seconds.
Add the heavy cream and broth. Simmer over medium-low heat until the sauce is reduced and slightly thickened, about 3 minutes.
Stir in a small amount of cheese at a time. Whisk it smooth after each addition, until the sauce is thickened for about 2 minutes. Adjust the seasoning with salt/black pepper if needed. Stir in the spinach and continue cooking until it's wilted.
Add the salmon fillets back into the pan and spoon the sauce over them OR pour the sauce over the salmon fillets right before serving.