Preheat oven to 400°F. Dress garlic with olive oil, salt and pepper, and wrap tightly in foil. Roast to tender, 40 minutes. Cool and mash cloves into paste.
Place chicken and all poaching ingredients in a pot with enough water to just cover chicken. Bring to a boil then reduce heat to a low simmer. Cook 1 hour, turning chicken once. Cool in poaching liquid then remove skin and bones from chicken. Pull meat into bite-sized pieces and strain stock; reserve.
Heat a soup pot over medium heat; add butter and melt. When butter foams, add mushrooms and lightly brown. Add celery, shallots, celery seed, thyme and pasted garlic; season with salt and pepper. Cover pan and sweat a few minutes then stir in flour. Cook a minute or so then whisk in sherry or wine. Add about 6 cups reserved poaching liquid and thicken a bit. Add chicken and cream, and season with nutmeg to taste. Reduce heat and thicken to your liking, serve with bread alongside.