Peel off the outer papery covering of the head of garlic. Using a sharp knife, then slice of 1/4″-1/2″ of the tops of the cloves, so that the inside of each clove is exposed.
Place the head on a square of aluminum foil. Drizzle the olive oil over the top of the cloves, and then use your fingers to spread it around well. Then fold up the foil over the top of the clove, so that it is fully enclosed. Either place the pouch directly on the oven rack, or you can place it on a pan (or muffin tins work well if you’re roasting multiple heads of garlic!).
Bake at 400 degrees for 30-35 minutes, until the garlic is soft and lightly browned. Remove from foil.
Heat olive oil in a large pot over medium-high heat. Add celery, onion and carrot and saute for 8-10 minutes, stirring regularly until the vegetables have softened.
Add flour and stir for another minute to combine. Then add chicken broth and bring to a boil. Reduce heat and simmer 15 minutes, stirring often.
Carefully squeeze the roasted garlic cloves out of the heads, and place them in the food processor (or blender). Add in one cup soup mixture and process until smooth. Returm processed mixture to pot and add in the thyme and oregano. Bring to a simmer.
Add cheese and stir slowly until melted. Season to taste with salt and freshly ground black pepper (or a tiny dash of white pepper), and serve. Garnish with chopped parsley if you’d like.