Preheat oven to 325°. Sprinkle roast lightly with salt and pepper; coat generously with flour. Pour oil into a large (at least 6-qt.), heavy ovenproof pot over medium-high heat. Add beef and cook, turning as needed, until browned all over, about 15 minutes total. Transfer to a plate.
Add chopped vegetables to pot and cook, stirring often, until beginning to brown, 10 to 12 minutes. Add broth, wine, thyme sprigs, and beef. Cover and bring to a boil, then transfer pot to oven. Bake until beef is tender when pierced, 3 to 3 1/4 hours, turning roast over once.
Meanwhile, melt butter in a large frying pan over medium-high heat. Add shallots and cook, stirring often, until beginning to brown, 3 to 4 minutes. Add mushrooms, increase heat to high, and cook, stirring often, until liquid has evaporated and mushrooms are beginning to brown, 12 to 14 minutes. Stir in thyme leaves and salt and pepper to taste.
Transfer beef to a platter; cover with foil and keep warm in a 200° oven. Pour braising liquid through a strainer into a wide frying pan. Skim off fat. Boil over high heat until reduced by about half, about 20 minutes. Stir in orange peel and salt and pepper to taste. Pour sauce into a bowl.
Cut beef into 1/2-in. slices and drizzle with a little sauce. Spoon mushrooms around meat and serve with remaining sauce on the side.
Note: Nutritional analysis is per serving.