In a large skillet over medium high heat, combine the olive oil, garlic, onions, and mushrooms. Saute for about 5 minutes, or until the onions are tender. Remove from heat and reserve for later.

In a large pot over high heat, combine the potatoes and carrots and add water to cover. Bring to a boil and reduce heat to low. Cover and simmer until vegetables are tender. Drain the water and add the milk. Continue to cook over low heat until milk starts to simmer.

Stir in the cheese soup, then stir in the flour slowly until mixed. Add 1 1/2 cups of the cheese, the reserved mushroom mixture, peas, corn and broccoli and heat through.