Remove the roast and vegetables to a platter. Skim excess fat from the cooking liquid. Whisk flour with a bit of water and stir into the pot juices to make a smooth gravy; simmer until thickened.
For the mashed potatoes, boil the potatoes in salted water until tender. Drain, then mash with butter, milk, salt, and pepper until smooth and creamy.
Serve slices of tender pot roast with carrots and a generous scoop of mashed potatoes, topped with rich homemade gravy.
