Sauté aromatics: In a large pot over medium heat, warm the oil. Add onion, carrot, and celery with a pinch of salt. Cook 5–7 minutes until softened.
Bloom flavors: Stir in garlic for 30 seconds. Add tomato paste and cook 1 minute, pressing it into the pan until slightly darkened.
Brown beef: Add beef, ½ tsp salt, and a few grinds of pepper. Cook, breaking up meat, until well browned, 5–7 minutes. Spoon off excess fat, leaving about 1 Tbsp in the pot.
Season base: Stir in Worcestershire and mustard, scraping up browned bits.
Simmer: Pour in broth and tomatoes. Bring to a lively simmer. Stir in macaroni and cook, stirring occasionally, 8–10 minutes until just al dente. If it thickens too quickly, add ½ cup hot water or more broth.
Finish creamy: Reduce heat to low. Stir in milk or cream. Add cheddar a handful at a time, stirring until melted and smooth before adding more. Do not boil.
Balance and serve: Taste and adjust salt. Add pickle brine or vinegar if you’d like extra brightness. Rest 3–5 minutes to thicken slightly. Ladle into bowls and top as you like.