Preheat the oven to 350°F. For the vegetable ragout, heat some olive oil in an 11-inch oven-safe frying pan and sauté the diced vegetables in it. Once the vegetables become tender, season them with salt & pepper and add in the diced tomatoes and rosemary. Mix everything together thoroughly, then let the vegetable ragout cook for 30 minutes, until any excess liquid has been cooked off. Once the sauce has cooked, turn off the heat and let it cool.
For the meatball-stuffed potatoes, stir together the ground beef, diced onions, minced garlic, egg, chopped parsley, and salt & pepper. Peel the potatoes and cut off the rounded sides, then make a deep slit in the center, making sure to save 1 large potato for later. For the best results, soak the potatoes in salted water for about 30 minutes to make them more flexible, then dry them off thoroughly. Coat the sliced potatoes with vegetable oil so that they keep their color, then fill them with the meatball mixture.
Arrange the stuffed potato slices in a circular pattern on top of the vegetable ragout in the oven-safe frying pan, alternating between 1 stuffed potato and 1 cheese cube, until the frying pan is almost filled.
For the final meatball-stuffed potato in the center of the frying pan, push an apple corer into the potato you set aside earlier, stopping halfway down the potato. Remove the round piece of potato from the center. Coat a cheese cube with the remaining meatball mixture and mold it into an ovular shape. Insert the cheese-stuffed meatball into the center of the potato you just cut.
Place the stuffed potato in the center of the pan. Transfer the oven-safe frying pan to the oven and bake the meatball-stuffed potato bake at 350°F for 45 minutes.