Heat 1 tablespoon olive oil in a large soup pot over medium-high. Brown ground beef, breaking into small pieces, then drain excess fat if needed.
Reduce heat, add 2 tablespoons butter, and 1¼ cups mirepoix. Sauté until vegetables soften and caramelize, about 8 minutes.
Add garlic, basil, parsley, and ground mustard (if using). Cook 1 minute.
Sprinkle flour over the mixture, stir, and cook 2 minutes to remove raw flour taste. Gradually whisk in chicken broth, then bring to a simmer.
Stir in elbow macaroni and cook until tender, about 10 minutes. Remove macaroni with a slotted spoon and set aside.
In the same pot, whisk in remaining ½ cup broth and 2 tablespoons butter. Add sour cream and remaining 1¼ cups milk-cream mixture. Bring to a slow simmer.
Gradually whisk in shredded Cheddar cheese until melted. Return macaroni to the pot, stir to coat evenly. Simmer 5-10 minutes until thickened. Season with salt and pepper.