Warm the olive oil in a large skillet on medium-high heat. Add the mushrooms and diced onion and cook until the mushrooms are nicely browned, about 5 to 7 minutes. Stir in the garlic and cook for another minute. Add the ground turkey to the pan and break it up as it cooks until there’s no pink left, roughly 6 to 8 minutes; drain any extra fat. Mix in the Italian seasoning, salt, and black pepper. Gradually add the spinach, stirring until all of it has wilted, about 2 to 3 minutes. Turn the heat down to low and blend in the heavy cream and grated Parmesan until the sauce is smooth and the cheese has melted. Serve right away.