1. Preheat oven to 325°F. Pat roast dry and season on all sides with salt and pepper. Sprinkle flour over roast and use your hands to spread it out and pat it evenly over meat.
2. Melt butter and 1 Tbsp. oil in a large roasting pan over medium-high heat on top of stove. Add roast and cook, turning with tongs, until browned on all sides, about 15 minutes total.
3. Place carrots and potatoes in a large bowl and toss with remaining 1 Tbsp. of oil. Place vegetables in roasting pan all around roast. Roast, stirring vegetables often, until a meat thermometer inserted into thickest part of roast registers 140°F for medium rare, 1 hour 30 minutes to 1 hour 45 minutes.
4. Transfer roast to a cutting board, tent loosely with foil and let rest for 10 minutes. Stick a sharp paring knife in carrots and potatoes to make sure they're easily pierced. If they're not, return roasting pan with vegetables to oven to continue cooking while roast rests.
5. Thinly slice roast and serve warm with carrots and potatoes.