Brown the bacon in a large pot or Dutch oven over medium heat for about 10 minutes until crisp, then lift it out with a slotted spoon and set it aside, keeping the drippings in the pot. Turn the heat up, add the ground beef in an even layer, leave it alone for 3 minutes to sear, then break it into chunky pieces. Drain off any excess fat, remove the beef, and set it aside with the bacon.
Sauté the onion, celery, and carrot in the same pot over medium heat for 10 minutes, until soft and sweet.
Add the garlic, Worcestershire sauce, yellow mustard, and ketchup and cook for 1 minute, stirring constantly.
Sprinkle the flour over the vegetables and stir for 1 minute to make the in-pot roux.
Pour in the broth, scraping the bottom of the pot to lift up the browned bits. Add the potatoes and the beef back in, bring to a gentle boil, then simmer, covered, for 15 minutes, until the potatoes are fork-tender.
Pour in the milk gently and simmer for 5 minutes, never letting it boil. Take the pot OFF the heat entirely and add the cheddar a handful at a time, stirring until each handful melts before the next goes in. Season with salt and pepper, ladle into bowls, and put the toppings bar on the table.