Heat 1 tablespoon olive oil in a large pot over medium-high.
Add 1/2 yellow onion, diced, and 1 minced garlic clove; sauté 3 minutes.
Reduce heat to medium; add 1 cup diced carrots and 2 celery stalks, diced. Sauté 5–7 minutes or until soft.
Sprinkle in 1/3 cup all-purpose flour; stir.
Add 2 cups low-sodium chicken broth; stir.
Add 2 cups 1% milk and 12 ounces pale ale (like Bass).
Cook 5–7 minutes or until foam disappears and soup thickens.
Stir in 8 ounces 50% reduced-fat sharp Cheddar cheese, shredded.
Simmer 15–20 minutes; serve with toasted whole-wheat bread and a garnish of Cheddar.