Preheat the oven to 400°F (200°C). Cut the top off the entire head of garlic, drizzle with olive oil, wrap in foil, and roast for about 30 minutes until soft and fragrant.
While the garlic roasts, pour chicken broth into a large stock pot and bring it to a gentle simmer over medium heat. Add salt and pepper to taste.
Once the garlic is done roasting and cool enough to handle, squeeze the soft garlic cloves out of their skins and mash them into a smooth paste. Stir the roasted garlic into the simmering broth, allowing the flavors to meld for about 10 minutes.
Add shredded cooked chicken to the broth and stir gently to combine. Let it warm through for 5 minutes, filling the kitchen with a savory aroma.
Meanwhile, cook the egg noodles in a separate pot of boiling water according to package instructions until just al dente. Drain and set aside.
Stir the noodles into the broth with chicken, then add fresh thyme or dried thyme at this stage for a bright herbal note. Mix gently to distribute evenly.
Taste the soup and adjust seasoning with additional salt, pepper, or a splash of lemon if desired. Let everything simmer together for another 5 minutes to develop flavor.
Serve the soup hot in bowls, garnished with a sprinkle of fresh herbs if you like. The broth should be flavorful and fragrant, with tender chicken and noodles wrapped in a silky, golden liquid.