Heat 2 tablespoons of the olive oil in a large Dutch with a lid oven over medium-high heat. Sprinkle the meat generously on all sides with salt and pepper and, working in batches if necessary, add to the pan. Sear the meat until it is well browned on all sides, about 8 minutes. Use tongs to help rotate the pieces of meat and remove them to a plate as they are seared. Set meat aside.
Add the onions and peppers to the same Dutch oven and cook until the vegetables start to become tender and golden, about 5 minutes. Add the grated tomatoes and cook, stirring occasionally, the onions and peppers have softened completely and most of the moisture has evaporated, another 5 minutes. Stir in the remaining 2 tablespoons of olive oil, the garlic, paprika and 2 teaspoons salt and cook until fragrant, about 1 minute more.
Return the seared meat to the pot along with the root vegetables and sliced salami; stir well. Add the chicken broth and increase the heat to high to bring the stew to a boil. Reduce to a simmer, cover and cook until the meat and vegetables are tender, 35 to 45 minutes. Stir in the cauliflower and red-wine vinegar, and continue cooking until the meat is tender enough to pull apart with a fork and the cauliflower is cooked, about 15 to 20 minutes more.
Season with salt and pepper, if necessary. Serve with toasted rustic bread brushed with olive oil and a sprinkle of chopped parsley.
Copyright 2016 Television Food Network, G.P. All rights reserved.