Preheat the oven to 325°F.
In a large skillet, heat a thin layer of EVOO over medium heat. Add the onions and garlic, and sweat until very soft and light caramel in color, 20-30 minutes.
Season the meat very liberally with salt and pepper. Over medium-high heat, heat a thin layer of EVOO in a Dutch oven and brown meat on all sides. Deglaze the pan with wine.
Arrange half the onions over the top of the meat; season with salt, pepper, and half the thyme. Arrange half the potatoes over the onions and dress with a liberal drizzle of EVOO, the rosemary, Parm, and salt and pepper to taste. Top the potatoes with half the tomatoes and their juices and season with salt and pepper. Scatter in a few basil leaves. Repeat the layers but do not add basil to the top layer of tomatoes.
Cover the pan and roast the meat in the oven for 2 1/2 hours. Turn off the oven but leave the pot to sit in the oven for another hour.
To serve, cut into chunks and spoon sauce over the meat.