Chop the onion and red potatoes into cubes. Cut the carrots and celery into slices. Mince the garlic finely. Add all the prepared vegetables to a 4 or 5 quart slow cooker.
In a bowl, toss the beef stew meat with flour, salt, and pepper until all pieces are coated evenly.
Heat a skillet on medium-high heat and add the cooking oil. Once hot, place the coated beef into the skillet and let it sear without moving until browned on one side. Stir and brown the beef on another side before transferring it to the slow cooker.
Reduce the skillet heat to medium-low and pour in the beef broth. Add Dijon mustard, Worcestershire sauce, soy sauce, brown sugar, rosemary, and thyme. Stir the mixture while cooking gently until the browned bits on the skillet bottom dissolve.
Pour this mixture over the vegetables and beef in the slow cooker and stir thoroughly to combine.
Cover the slow cooker with its lid and cook on high for four hours or on low for eight hours.
Once cooked, the beef and vegetables should be tender. Stir the stew well to help the potatoes break down slightly, thickening the gravy. Taste and adjust seasoning if needed. Serve warm.