Preheat oven to 350 degrees F.
Heat EVOO over medium heat in saute pan. Add the butter to the oil and when it foams, add the garlic, thyme, parsley and pepper and swirl for 1 to 2 minutes. Place the bread in a large bowl and toss with the butter sauce and half the cheese. Arrange on a baking sheet and bake until deeply golden and crispy, 20 minutes. The croutons can be stored wrapped in foil at room temp or in an airtight container for several days.
Bring a couple of inches of water to boil in a deep skillet. Salt the water and add the broccoli. Cook to tender-crisp, 5 minutes; drain. The broccoli can be stored in the fridge in a plastic bag for several days.
To assemble and bake the casserole, preheat the oven to 400 degrees F and arrange the croutons in a dish. Top with the broccoli, chicken, soup and remaining 3/4 to 1 cup Parm. Bake until hot throughout and golden on top, 35 to 40 minutes.
For the poached chicken stock: Place the chicken, carrots, celery, onion, garlic, lemon, herb bundle, peppercorns and salt in a pot, cover with water and bring to a low boil. Reduce heat to simmer and simmer for 1 hour minimum. Cool the chicken in the broth. Remove the chicken and cool. Separate the meat and pull or chop into bite-size pieces. Reserve for the Broccoli Casserole preparation. The chicken can be stored in a plastic bag in the fridge for 4 days. Strain the stock and reserve for soup.
For the soup: Heat a soup pot over medium heat. Melt the butter and when it begins to foam, add the celery, onions and garlic; season with celery salt and pepper. Add the fresh bay leaf to pot, partially cover, and cook until very tender and soft, about 20 minutes, stirring occasionally.
Add the potatoes, celeriac and stock and bring to a boil. Reduce heat to a low rolling boil and simmer, partially covered, for another 20 minutes, then puree with an immersion blender. Cool the soup and store for a make-ahead meal.
Place the soup in a stockpot and stir in the cream. Bring to simmer and taste to adjust seasoning.
Yield: 4 to 6 servings (plus 3 to 4 cups to reserve for Broccoli Casserole)