Fire up your grill to medium heat. Brush the mushrooms with the olive oil. Sprinkle with a bit of fine sea salt.
Place the mushrooms on the grill, stem side facing down. Grill for about 10 minutes, or until the portobellos start to become tender.
Meanwhile, combine the quartered cherry tomatoes, chopped spinach and basil, oregano, sea salt and pepper in a bowl. Toss well.
Once mushrooms are ready to flip over, use a spatula to flip them, then remove from the grill. Spoon the marinara and spinach/tomato mixture evenly into the mushrooms, then sprinkle the shredded mozzarella on top.
Return the mushrooms to the grill and cook until the cheese looks bubbly and the mushrooms are tender, 5-10 minutes. Enjoy while they're warm!