Preheat the oven to 375 degrees F. Butterfly the pork: Cut in half horizontally, almost all the way through, then open it like a book so the roast is flat. Season with salt and pepper; sprinkle with 2 tablespoons flour. Heat 1 tablespoon olive oil in a skillet over medium-high heat. Brown the pork, about 3 minutes per side. Transfer to a baking dish (reserve the skillet) and bake until a thermometer inserted into the center registers 140 degrees F, 15 to 20 minutes. Let rest on a cutting board, 5 minutes.
Add the mushrooms and 1/4 teaspoon salt to the skillet and cook until golden brown, about 8 minutes. Add the remaining 1 tablespoon flour and cook, stirring, 1 minute. Add the broth and marsala and bring to a boil. Add the cream and boil until the sauce thickens, about 8 minutes. Off the heat, stir in 2 teaspoons lemon juice and the parsley.
Heat the remaining 1 tablespoon olive oil in a pot over medium-high heat and cook the spinach until wilted, 3 to 4 minutes. Stir in the remaining 2 teaspoons lemon juice and season with salt and pepper. Slice the pork. Serve with the mushroom sauce and spinach.