Boil, pan-sear, or grill hot dogs until heated through. Meanwhile, heat oil/fat in a skillet over medium-high heat. Add the onion, mushrooms, garlic, dried oregano, salt, & pepper and saute, stirring occasionally, until the onion is translucent and the mushrooms are soft. Preheat oven to 400 F. Assemble each hot dog by placing it in a bun, topping it with mushroom and onion mixture, a generous drizzle of pizza sauce, then topping with mozzarella. Place assembled dogs on a baking sheet and place them in the oven until the cheese is melted. Remove from the oven and sprinkle with fresh basil and oregano.