Heat oven to 300°. Put currants and half of the madeira into a medium bowl and set aside to let soften for 10 minutes. Meanwhile, heat 4 tbsp. of the butter in a large skillet over medium heat. Add thyme and shallots and cook until softened, about 10 minutes. Transfer shallot mixture to bowl of currants; add breadcrumbs, capers, and salt and pepper. Stir well. Set the shallot-caper stuffing aside.
Lay veal breast flat on a cutting board and season all over with salt and pepper. Top with the stuffing; spread out evenly, leaving a 1" border around the edges. Roll up veal breast and tie snuggly with butcher's twine down the length of the roast at 1 1⁄2" intervals.
Heat remaining butter and olive oil in a large skillet over medium-high heat. Add veal and cook, turning occasionally, until deep golden brown all over, 10–12 minutes; transfer veal to a small roasting pan. Add half of the wine to skillet and cook, scraping up any browned bits, about 1 minute; pour over veal. Roast, basting every 20 minutes or so with any pan juices, until a meat thermometer inserted in the thickest part of the roast registers 165°, about 1 3⁄4 hours.
Transfer roast to a large platter, cover with foil and set aside. Set roasting pan over medium-high heat on stove. Add beef stock and cook, scraping up any browned bits, for 2 minutes. Transfer pan juices to a small saucepan; skim off and discard any fat. Add remaining madeira and wine and cook over medium heat until just thickened, about 5 minutes. Season with salt and pepper; keep warm.
For easy carving, leave butcher's twine on and cut veal into thick slices. Remove twine and serve with pan juices.