Cook bacon in a large pot over medium-high heat until crisp. Remove bacon with a slotted spoon to a paper-towel-lined plate; set aside.

Pour off all but 2 tablespoons of bacon drippings. Add onion, celery, and garlic to drippings in pot and sweat over medium heat until onion is softened, about 5 minutes. Stir in flour and cook 1–2 minutes. Add potatoes, dry mustard, and paprika; cook, stirring to coat potatoes, 1 minute.

Stir in broth, Worcestershire, and Tabasco. Bring to a boil, reduce heat to medium-low, and cook, partially covered, until potatoes are soft, 10–15 minutes.

Coarsely mash potatoes, then stir in Cheddar and half-and-half until Cheddar is melted, 2 minutes.

Remove soup from heat; season with salt, black pepper, and cayenne. Garnish servings with bacon and scallions.