Preheat oven to 375 degrees F (190 degrees C). Lightly grease a medium baking dish.
Place the beef and onion in a skillet over medium heat. Season with rosemary and basil. Cook until beef is evenly brown; drain grease. Mix in tomato sauce, diced tomatoes, and mixed vegetables. Cook and stir until vegetables are heated through. Transfer to the baking dish.
Place potatoes in a pot with enough water to cover, and bring to a boil. Cook 10 minutes, or until tender. Remove from heat and drain. Mix butter, Romano cheese, garlic, salt, oregano, and milk into the pot. Mash together with a potato masher. Top beef and vegetables with the mashed potatoes.
Bake 30 minutes in the preheated oven. Turn oven to broil, and continue cooking 3 minutes, until potatoes are golden brown.