Scrub the potatoes. Cut them lengthwise into ¼ -inch sticks. Transfer them to a large bowl and add cold water, vinegar and mix well. Soak the potatoes for 30 minutes.
Preheat the oven to 200°F (93°C). Oil the baking sheets with the olive oil.
Drain the potatoes and spread them on the prepared baking sheet. Set the baking sheets in the oven and dehydrate for about 25 minutes. Set aside.
In a large skillet, heat the olive oil over high heat. Add the ground meat and cook until well browned. Add the minced garlic, minced onion, chopped celery and carrot. Seasoning with salt and pepper. Whisk in flour and mix well.
Add the chicken stock, red wine and Balsamic vinegar Whisk until well combined. Bring to a boil, then reduce the heat to a simmer and cook for 20 minutes until the gravy has thickened and the meat is tender. Finish with 1/2 cup of tomato sauce and mix. Reserve and keep warm.
In a large pot, pour 4 cups olive oil. Heat the oil over high heat to 300°F (150°C). Cook the potatoes in the oil until lightly golden. Then lift the potatoes from the oil, and transfer to a bowl. Let cool for 10 minutes.
Increase the temperature of the oil to 375°F (190°C). Fry the potatoes in the hot oil until golden brown and crispy. Drain well and transfer the fries to a large bowl. Seasoning with salt and pepper.
Place the hot crispy fries on a large platter. Sprinkle with the cheese then ladle the gravy over the top. Garnish with parsley and serve.