01 - Cook macaroni in salted boiling water until just al dente. Drain thoroughly and set aside.
02 - Melt butter in a large pot over medium heat. Add diced onion and grated carrot, cook until softened, approximately 4 minutes. Add minced garlic and cook for an additional minute until fragrant.
03 - Sprinkle flour over the vegetables, stirring constantly to coat evenly. Cook for 1-2 minutes to eliminate raw flour taste, creating a light roux.
04 - Slowly whisk in milk and vegetable broth, ensuring smooth incorporation without lumps. Bring mixture to a gentle simmer while stirring frequently.
05 - Add dry mustard powder, salt, and pepper to taste. Reduce heat to low to maintain gentle temperature.
06 - Gradually stir in shredded cheeses, one handful at a time, continuing to stir until completely melted and soup achieves smooth, velvety consistency.
07 - Add cooked macaroni to the cheese soup, heating gently for 2-3 minutes. Adjust seasoning if necessary. Serve immediately, garnished with chopped chives.