Cut the onion and red potatoes into cubes, slice the carrots and celery thinly, and finely chop the garlic. Put all the chopped vegetables into a 4-5 quart slow cooker.
In a separate bowl, coat the beef stew meat evenly with flour, salt, and black pepper by tossing it well.
Warm a large skillet over medium-high heat, add the cooking oil, and swirl to cover the pan. Place the floured beef chunks in the skillet and let them brown without stirring for a few minutes. Turn the beef to brown on another side, then transfer the meat to the slow cooker.
Reduce the heat to medium-low under the skillet and pour in the beef broth. Stir in Dijon mustard, Worcestershire sauce, soy sauce, brown sugar, rosemary, and thyme. Simmer gently, scraping the skillet to lift any browned bits, until the mixture is well combined.
Pour this sauce over the contents of the slow cooker and stir everything together thoroughly.
Cover the slow cooker and cook on the high setting for 4 hours, or on low for 8 hours.
Once finished, check that the beef and vegetables are tender. Stir the stew to help the potatoes break down slightly and thicken the sauce. Adjust seasoning if needed and serve hot for a comforting meal.