Heat olive oil in a large pot over medium heat; cook and stir onion and garlic until onion is transparent, 5 to 7 minutes.
Stir chicken broth, potatoes, and carrots into onion mixture. Bring to a boil, reduce heat to medium-low, and simmer until carrots and potatoes are tender, 10 to 15 minutes.
Strain vegetables from chicken broth with a slotted spoon. Puree vegetables in a food processor, working in batches.
Return pureed vegetables to broth and bring to a simmer.
Stir cauliflower, dill, and mustard powder into broth mixture.
Stir Cheddar cheese into broth mixture, in small batches, until cheese is melted, 5 to 10 minutes. Season with salt and black pepper.