Preheat oven to 400°F (200°C). Slice off the very top of the garlic head, exposing the cloves. Drizzle with 1 tsp olive oil, sprinkle with a pinch of salt and pepper. Wrap loosely in aluminum foil and roast for 30-35 minutes, or until cloves are very soft and golden brown. Let cool slightly, then squeeze the softened garlic from their skins into a small bowl. Mash with a fork to form a paste.

While garlic roasts, pat chicken thighs dry with paper towels. Season generously with 1/2 tsp salt and 1/4 tsp black pepper. Heat 1 tbsp olive oil in a large Dutch oven or stockpot over medium-high heat. Add chicken in a single layer (cook in batches if necessary to avoid crowding) and sear for 3-4 minutes per side until golden brown. The chicken does not need to be cooked through. Remove chicken to a plate and set aside.

Reduce heat to medium. Add the remaining 1 tbsp olive oil to the pot. Add diced onion, carrots, and celery. Sauté for 8-10 minutes, stirring occasionally, until vegetables soften. Add the 1/4 cup all-purpose flour to the vegetables and stir constantly for 1-2 minutes to cook out the raw flour taste, creating a roux.

Gradually whisk in the chicken broth, ensuring no lumps form. Add the bay leaf and dried thyme. Bring the soup to a simmer, scraping any browned bits from the bottom of the pot. Stir in the roasted garlic paste.

Return the seared chicken pieces to the pot. Reduce heat to low, cover, and simmer for 20-25 minutes, or until chicken is cooked through and tender, and flavors have melded. Remove the bay leaf.

Stir in the heavy cream and fresh lemon juice. Taste and adjust seasoning with additional salt and black pepper if needed. Stir in the fresh parsley and dill just before serving.

Ladle the Unbelievable Chicken soup into bowls and serve hot. Garnish with extra fresh herbs if desired.