Chop onion. Heat oil in a large pot and then add onions. Saute for 3-4 minutes, stirring frequently. Stir in thyme, garlic powder, and pepper; then, add broccoli and vegetable stock. Boil for 15 minutes, stirring occasionally.
Toss cheese with corn starch until evenly coated; set aside.
Reduce heat to low. At this point, if you like a really creamy consistency, you may mash the soup to break down the broccoli. This can be done with a potato masher or a handheld immersion blender.
Stir in milk and cheese and simmer for 10 minutes, stirring frequently, until cheese has melted and soup has thickened.
Serve soup hot with Italian bread and kiwi slices on the side.