Heat oil in a pot set over medium heat. Add onions and garlic and cook until tender. Mix in flour. Slowly stir in stock. Add potatoes and herbs and bring to a simmer. Cook until potatoes are very tender, about 20-25 minutes. Remove bay leaf. Puree the mixture in a food processor or blender, and then return to soup pot. Stir in milk and 1 cup of the cheese and bring back to a simmer. Season to taste and pour in to soup bowls. Garnish top with a little grated cheese and chopped greens onions.