Over medium heat in a large pot or dutch oven, add olive oil, garlic, and onions. Cook for 3-4 minutes or until the onions are translucent and golden. Transfer to a small bowl or plate and set aside.
To the same pot or dutch oven, add butter. Once melted, sprinkle the flour in. Keep whisking until it is smooth and starts to bubble, about 2 minutes.
Pour in the chicken broth, heavy cream, and milk. Whisk together. Then add back the onion and garlic mixture along with the broccoli, carrots, mustard powder, smoked paprika, dash of nutmeg, and a dash of cayenne. Whisk again, drop heat to low, cover, and let simmer for 15-20 minutes, or until the broccoli and carrots are tender.
Remove the lid and add the cheddar cheese. Mix together. Then add black pepper and salt to taste. Stir.
Pour into bowls and serve with crispy bread to dip in!