Preheat the oven to 375°F.
In a large cast-iron skillet (or Dutch-oven) over medium, heat the olive oil. Add the diced onion and cook until soft and translucent, about 5 minutes. Add the garlic, basil, and oregano, cooking for another 30 seconds. Remove from heat.
Stir in the rest of the ingredients in order listed, except for the vegan cheese. Mix well. Cover tightly with tin foil (or fitted lid), and bake for 35-40 minutes, or until the rice is cooked.
Carefully remove the foil, and sprinkle the grated cheese over the top. Cover again and bake another couple of minutes so the cheese melts. Enjoy! Refrigerate leftovers in an airtight container for 3 days, or freeze for up to 3 months.