In a large pot, sauté onion in oil or butter until golden. Add vegetables, water, and seasonings; stir to combine.

Bring to a boil and lower heat to medium; cook for 40 minutes or until vegetables are cooked through. Reduce heat to medium-low; add milk and bring to a boil again. Remove from heat.

After ladling into individual bowls, garnish with a teaspoon of shredded cheese.