Start by heating the olive oil and butter in a large skillet over medium-high heat. Add the chopped onion and cook until soft and translucent. Stir in the mushrooms, garlic, and Italian seasoning, letting the mushrooms cook until they release moisture and develop a golden brown color.
Pour in the broth and heavy cream, stirring to combine everything smoothly. Add the tortellini directly into the sauce and stir to coat. Lower the heat slightly, cover the skillet, and let the tortellini cook for about 5 minutes while the sauce thickens.
Uncover the skillet and add the fresh spinach. Stir until it wilts into the sauce. Add the grated Parmesan, stirring until it melts fully and blends into the creamy mixture. Taste and adjust with salt and pepper before serving.