Pat the salmon dry and season both sides with salt and pepper. Dredge each piece lightly in flour, shaking off excess.
Heat the olive oil and butter in a large skillet over medium-high heat until hot and the butter is melted.
Add the salmon to the hot skillet and cook about 3 minutes per side, until golden and nearly cooked through; transfer to a plate and set aside.
Lower the heat to medium and add the chicken broth, softened cream cheese, and minced garlic to the skillet; stir often until the cream cheese melts into a smooth sauce.
Stir in the chopped artichoke hearts and fresh spinach; cook until the spinach wilts. If the sauce becomes too thick, add a splash more chicken broth to reach desired consistency.
Mix in the grated Parmesan, return the salmon to the skillet, and cook a few more minutes until the salmon is cooked through and flakes easily with a fork. Taste and adjust salt and pepper, then serve immediately.