Preheat your oven to 400°F (200°C).
Slice the top off the head of garlic, wrap it in aluminum foil, and drizzle with 1 tablespoon of olive oil.
Place the wrapped garlic in the oven for about 30–35 minutes or until the cloves are soft and golden.
In a mixing bowl, combine the softened goat cheese, cream cheese, sour cream, and remaining olive oil.
Squeeze the roasted garlic cloves out of their skins and add them to the mixture.
Stir in fresh thyme leaves along with salt and pepper to taste.
Using a hand mixer or food processor, blend all ingredients until smooth and creamy.
Spoon the dip into your desired serving dish and smooth out the top with a spatula.
If desired, garnish with additional thyme leaves or a drizzle of olive oil.
Serve warm or at room temperature.