In a large pot or Dutch oven, melt the butter over medium heat. Add the peeled garlic cloves and cook, stirring occasionally, until they are softened and lightly golden, about 10-15 minutes. Do not let them burn.
2 pounds garlic
Sprinkle the flour over the softened garlic and stir well to coat. Cook for 1-2 minutes, stirring constantly, to cook out the raw flour taste.
2 pounds garlic
Gradually whisk in the chicken broth, scraping up any browned bits from the bottom of the pot. Add the thyme sprigs, salt, and pepper. Bring to a simmer, then reduce heat to low, cover, and cook for at least 30 minutes, or until the garlic is very tender.
2 pounds garlic
Remove the thyme sprigs. Using an immersion blender, carefully blend the soup until smooth. Alternatively, you can transfer the soup in batches to a regular blender (be very careful with hot liquids).
Ladle the soup into oven-safe bowls. Top each bowl with toasted baguette slices and grated Gruyere cheese.
2 pounds garlic
Place the bowls on a baking sheet and broil for 1-2 minutes, or until the cheese is melted and bubbly and the croutons are golden brown. Watch carefully to prevent burning.
Serve immediately.
Notes
For an even richer flavor, you can roast the garlic cloves before adding them to the pot. Simply toss the peeled cloves with a little olive oil and roast at 400°F (200°C) for 20-30 minutes until soft and fragrant.