01 - Cook elbow macaroni in salted boiling water until al dente. Drain thoroughly and set aside.
02 - Melt butter in a large pot over medium heat. Add diced onion and grated carrot, cooking until softened, approximately 4 minutes. Stir in minced garlic and cook for 1 additional minute until fragrant.
03 - Sprinkle flour over the sautéed vegetables, stirring constantly to coat evenly. Cook for 1-2 minutes to eliminate raw flour taste.
04 - Gradually whisk in whole milk and vegetable broth, ensuring smooth incorporation without lumps. Bring mixture to a gentle simmer while stirring frequently.
05 - Stir in dry mustard powder, salt, and black pepper. Reduce heat to low setting.
06 - Add shredded sharp cheddar and mozzarella cheeses gradually, one handful at a time. Stir continuously until completely melted and soup achieves silky consistency.
07 - Add cooked macaroni to the cheese soup base. Heat gently for 2-3 minutes, stirring occasionally. Adjust seasoning to taste. Serve immediately, garnished with chopped chives.