1. Season the meat with salt and pepper. Brown the meat on all sides in the hot oil a deep skillet (or in the Cuisinart 3-in-1 4-Quart Cooker—I set mine at 375° when browning). Transfer the meat to a plate.
2. Reduce the heat to medium. If the pan is dry, add another tablespoon of oil. Add the onion and carrot; cook, stirring, until slightly softened, about 3 minutes; add the garlic and cook, stirring, until fragrant, about 30 seconds more. Add the wine, beef broth, Balsamic vinegar, and herbes de Provence. Bring to a boil, stirring to loosen any browned bits from the bottom of the pot. (If doing this step on the stovetop, pour the liquid into the cooker at this point.).
3. Place the browned meat in the cooker. Cook on low for 8 hours OR on high for 5 hours or until the meat is tender.
4. Transfer the roast to a cutting board and cover with foil to keep warm. Set the cooker on 375° (or transfer the cooking liquids to a clean saucepan). Work the butter into the flour to form a paste (a beurre manié). Bring the liquid to boil; whisk in the beurre manié bit by bit until sauce is as thick as you like. Serve sauce with meat.