Peel carrots, cut into 3-inch chunks, and cut large pieces in half again lengthwise.

Peel shallots and cut in half through the root.

Heat oil in a large frying pan over medium-high heat (for best browning, do not use a nonstick pan). Sprinkle chuck roast with salt and pepper. Brown roast on both sides in hot oil, turning as needed, 6-8 minutes total.

Transfer roast to a 6-qt. slow cooker. Top with carrots and shallots.

Pour red wine into hot frying pan used to brown roast. Scrape any browned bits from the bottom of the skillet using a wooden spoon. Stir in vinegar, brown sugar, beef base, and tomato paste. Pour mixture over roast in slow cooker.

Top roast and vegetables with fresh thyme and rosemary.

Cover slow cooker and cook on low setting until roast is tender when pierced with a fork, 6 hours.

Transfer roast from slow cooker to a cutting board and vegetables to a serving platter.

Whisk together flour and cold water in a small saucepan. Measure 1 cup cooking liquid and strain into pan, whisking. Bring to a boil, whisking often. Reduce heat and simmer, whisking occasionally, until gravy is thickened, 5 minutes.

Slice meat and arrange on platter with vegetables. Spoon gravy on top. Scatter fresh herbs over roast and vegetables, and serve.