Preheat the oven to 325 Degrees F. Place the flour in a medium-sized bowl and season salt and pepper. Add the beef and toss to coat. Shake off excess flour and set beef on plate. Reserve leftover flour.
Place the oil in a Dutch oven or ovenproof pot set over medium-high heat. When hot, add the beef, in batches, brown on all sides, and then set on a clean plate.
Lower the heat under the pot to medium. Add the onion, carrot, celery and garlic and cook 3 minutes. Mix in the tomato paste and 2 Tbsp. of the reserved flour; discard the rest. Slowly, stirring constantly, mix in the stock. Mix in the thyme, bay leaf and Worcestershire.
Return the beef to the pot and bring to a simmer. Cover and cook in the oven for 75 minutes, or until the meat is tender.
While the stew cooks, boil the potatoes until very tender. Drain well, and then thoroughly mash. Vigorously mix in the butter and milk; season with salt and pepper.
When ready, spoon the stew into bowls, pipe or dollop some potatoes on top, sprinkle with parsley and serve.