Season pork chops on both sides with salt and pepper. In a large skillet over medium heat, heat oil. Add pork chops and cook until golden and cooked through. Remove from skillet and place on a plate to keep warm.
Add mushrooms to skillet and cook until softened, 5 minutes, then add garlic and cook until fragrant, 1 minute more.
Add heavy cream, Parmesan, oregano, and a pinch of red pepper flakes. Season with salt and pepper. Bring sauce to a simmer and cook until thickened, about 3 minutes. Add spinach and cook until wilted, 2 minutes more.
Return pork chops to skillet and cook until warmed through, 5 minutes.