Preheat your oven to 375–400°F (190–200°C). Slice the top off a head of garlic, drizzle with olive oil, and season with salt and pepper. Wrap in foil and roast for 40–45 minutes, until soft and fragrant.

Bring a large pot of water to a boil and cook the peeled and cubed russet potatoes until fork-tender, about 15-20 minutes. Drain and set aside.

In a large pot over medium heat, melt 4 tablespoons of butter, add diced onion and leek, and sauté for 5-7 minutes until softened.

Lower heat and sprinkle ¼ cup of all-purpose flour over onions and leeks, stirring continuously for about 1 minute. Gradually whisk in 4 cups of broth, 1 cup of milk, and ½ cup of heavy cream. Add thyme, salt, and pepper, and heat until slightly thickened.

Add cooked potatoes and squeezed roasted garlic to the pot. Blend everything using an immersion blender until smooth. Adjust consistency with additional broth if needed.

Butter one side of each slice of bread. Place grated Gruyère cheese on the non-buttered side of two slices, top with other slices, buttered side facing out. Cook sandwiches until golden brown in a skillet, about 5 minutes per side, then cut into croutons.

Ladle the soup into warm bowls. Garnish with additional grated Parmesan, chopped chives, and croutons.