In a large saucepan cook onion in hot oil over medium heat until tender. Sprinkle flour over onion and stir to coat. Add chicken broth, asparagus, milk, garlic, and potatoes.
Cook and stir until thickened and bubbly; reduce heat.
Simmer, covered, for 10 to 12 minutes or until vegetables are tender, stirring occasionally. Add cheddar and sour cream; stir until cheese is melted.