Prepare the veal: Preheat the oven to 350 degrees F. Heat 3 tablespoons vegetable oil in a large skillet over medium-high heat. Add the onions, bell peppers and 1 teaspoon salt and cook, stirring, until soft, 8 to 10 minutes. Add the tomatoes and cook until most of the liquid evaporates, about 5 minutes. Stir in the paprika, then add the wine and boil until reduced by half, about 3 minutes. Add the chicken broth; transfer the mixture to a large baking dish.
Pat the veal dry; sprinkle with 2 teaspoons salt and 1 teaspoon pepper. Wipe out the skillet, add 1 tablespoon vegetable oil and heat over medium-high heat. Cook the veal in 2 batches until browned, 3 to 4 minutes per side, adding the remaining 1 tablespoon vegetable oil between batches. Transfer the veal to the baking dish, cover with foil and bake until tender, 2 hours to 2 hours, 30 minutes.
Meanwhile, prepare the vegetables: Heat the sugar and 1 1/2 tablespoons olive oil in a skillet over medium-high heat until the sugar melts. Add the cipollini onions and cook, tossing, until browned, 3 to 5 minutes. Add the wine, 1/4cup water and a pinch of salt. Reduce the heat to medium low and cook, partially covered, until tender, about 20 minutes. Uncover and cook over medium-high heat, stirring until glazed, about 5 more minutes.
Heat the remaining 1 tablespoon olive oil in a separate skillet over medium heat. Add the mushrooms and cook, stirring, until tender, 3 to 5 minutes. Add the parsley, dill and salt and pepper to taste. Keep warm.
Transfer the veal to an ovenproof platter, cover with foil and keep warm in the oven (turn the oven off). Strain the liquid from the baking dish, discarding the solids. Skim off 1 tablespoon fat from the strained liquid; transfer the fat to a saucepan over medium-high heat. Add the flour and cook, stirring, 1 minute. Whisk in the liquid and simmer, whisking occasionally, until thickened, 10 to 15 minutes. Spoon the sauce over the veal and serve with the mushrooms and onions