Preheat oven to 325°F. In the same skillet, heat the remaining 1 tablespoon of olive oil. Add the onion and sauté until translucent, 1 to 2 minutes. Add the mushrooms and sauté until cooked, about 5 minutes. Add the spinach in batches and cook until wilted, another 1 to 2 minutes. Season with 1/4 teaspoon of salt and 1/8 teaspoon of black pepper, and remove from heat.
Transfer the mushroom-spinach mixture to the baking dish.