Heat oil or butter in large pot. Once melted, add onions, garlic and carrots and cook until soft, about 5 minutes.
Add broccoli. Cook for additional 5 minutes, then season with salt, pepper, paprika, mustard and hot sauce. Add milk and broth. Simmer over medium heat for 10 minutes.
Mix cornstarch and cold water. Pour into the pot and whisk until smooth. Let it cook to thicken.
Add cheese and cook just until cheese is melted. Adjust seasoning. Serve.