In a large soup pot, sauté the onion, garlic and celery (with leaves if using) in the olive oil and bacon until bacon renders its fat and vegetables soften.
Add the thyme, cauliflower, broccoli, and chicken broth.
Bring to a boil, then reduce heat, cover and simmer for 15 minutes.
Stir cornstarch into evaporated milk until smooth then add to soup. Allow to return to a boil for a minute to thicken.
Remove from heat and add cheese, stirring constantly to allow it to melt.