Preheat your oven to 400°F (200°C). Slice off the top of the garlic head, drizzle with 1 teaspoon of olive oil, wrap in foil, and roast for 30-35 minutes until soft.
While garlic is roasting, let feta and cream cheese sit at room temperature for about 15 minutes to soften.
Once garlic is done, let it cool slightly. Squeeze the roasted garlic into a blender or food processor, then add softened feta, cream cheese, 2 tablespoons of olive oil, and 1 tablespoon of lemon juice.
Blend on high speed until smooth and creamy. If too thick, add more olive oil or a splash of water to adjust consistency.
Fold in fresh thyme leaves and chopped parsley. Transfer to a serving bowl, garnish with herbs if desired, and serve immediately or refrigerate.