01 -
Heat butter in a large pot over medium-high heat. Add onion, carrot, celery, and a couple large pinches of salt and pepper. Cook, stirring frequently for 8 minutes.
02 -
Add garlic, ground mustard, cayenne pepper, and flour, and cook for 1 minute.
03 -
Add a couple splashes of broth to deglaze the pan and scrape all the flavorful bits off the bottom. Add potatoes, remaining broth, and a couple large pinches of salt and pepper.
04 -
Bring to a simmer over medium-high heat. Reduce heat to low and simmer for 12-15 minutes, stirring every few minutes, until the potatoes and carrots are cooked through and tender.
05 -
Remove from heat and stir in cream, shredded cheese (reserve some for garnish), and vinegar until cheese melts.
06 -
Season to taste with salt and pepper. Garnish with chives and shredded cheese before serving.