In a large pot, melt the butter over medium heat. Add the diced onion and cook for 3–4 minutes, until softened and fragrant. Stir in the garlic and cook for one more minute.
Add the cauliflower, broth, dijon mustard, and a generous pinch of salt. Cover with a lid and cook for 5-10 minutes, until the cauliflower is fork tender. Use an immersion blender to blend until smooth (or transfer carefully to a blender).
Return the soup to low heat and stir in the milk and shredded cheddar until the cheese is melted and creamy. Taste and add more salt if needed.
If you’re adding pasta, bring a separate pot of salted water to a boil and cook according to package instructions. Drain and add to the soup just before serving.
Ladle into bowls and drizzle with olive oil. Top with chopped dill, chives, and black pepper.
