Start by heating the oil in a large pot or Dutch oven over medium heat. Once it's hot, add the ground meat, season it lightly with salt and pepper, and cook it until it's browned throughout. Drain any excess fat, if needed, then remove the meat to a seperate plate, cover with foil and set it aside.

Add the butter to the pot. Once it melts, add the onion, celery and shredded carrot. Cook, stirring often, until they begin to soften, about 5-7 minutes. Then add the garlic, ketchup, mustard and Worcestershire sauce. Cook and stir for another couple of minutes. Then sprinkle the flour over the top and cook and stir for another minute or two.

Increase the heat to med-high and stir in the broth and seasonings. Let it come up to a low boil, then stir the meat back in, along with the potatoes. Reduce the heat back down to medium-low and let this simmer until the potatoes are fork tender. Then stir in the milk and the shredded cheese, stirring to incorporate and melt the cheese in.