Begin by patting the salmon fillets dry with a paper towel. Season both sides with salt and pepper. Dredge each piece lightly in flour, shaking off any excess.
In a large skillet, heat the olive oil and butter over medium heat. Once the butter has melted and starts to bubble, add the salmon fillets, skin-side down. Cook for about 4-5 minutes on each side until golden brown and cooked through. Remove the salmon from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Pour in the chicken broth and scrape up any browned bits from the bottom of the pan. Stir in the softened cream cheese until melted and combined.
Mix in the chopped artichoke hearts and fresh spinach. Cook until the spinach wilts down, about 2-3 minutes. Stir in the grated Parmesan cheese and season with salt and pepper to taste.
Return the salmon to the skillet, spooning the creamy spinach and artichoke mixture over each piece. Allow everything to heat through for a minute. Serve immediately, garnished with additional Parmesan if desired.
