Preheat your oven to 375°F (190°C). Slice the tops off two whole heads of garlic, drizzle them with olive oil, and wrap them snugly in aluminum foil. Place the foil packets on a baking sheet and roast for 35-40 minutes until golden brown and soft.

While the garlic roasts, heat 2 tablespoons of olive oil with 1 tablespoon of butter in a large soup pot over medium heat. Add 2 cups of diced yellow onions and cook for 15-20 minutes until they turn rich and golden.

Once the garlic is tender, squeeze the cloves out of their skins and add them to the pot with the caramelized onions. Toss in 1 teaspoon of fresh thyme, a bay leaf, and a sprinkle of salt and pepper. Pour in 4 cups of vegetable broth, bring to a gentle boil, then simmer uncovered for 15-20 minutes.

Remove the bay leaf from the pot, then use an immersion blender to purée the soup to your desired consistency.

Return the soup to low heat and stir in 1 cup of milk or cream, heating gently without boiling. Adjust seasoning as needed.

Ladle the soup into bowls, garnish with freshly ground black pepper and chopped parsley. Serve with toasted crusty bread.