Preheat the oven to 400F and place a rack in the centre of the oven. Tear off two squares of foil and set aside.
Using a sharp knife, carefully cut the tops off the heads of garlic to expose the cloves. Place a head of garlic in the centre of each of the foil squares. Drizzle the garlic heads with olive oil. Bring up the corners of the foil to enclose the garlic, wrapping the garlic snuggly in the foil. Place the foil wrapped garlic heads directly on the oven rack and roast until the garlic cloves are golden and soft when squeezed, about 30-45 minutes (depending on size and freshness of garlic). Remove the garlic heads from the oven, unwrap and allow to cool to room temperature. (Make ahead: Garlic can be roasted up to 3 days in advance and stored in a covered container in the fridge until ready to use.)
Add the feta cheese, cottage cheese, cooled roasted garlic, thyme, lemon juice and 1 Tbsp of olive oil to a small food processor. Process the ingredients until smooth. Transfer the whipped feta to a serving dish and spread evenly with the back of a spoon. Drizzle with additional olive oil and sprinkle with fresh thyme leaves to garnish. (Make ahead: This dip is delicious right after you make it, but it's even better if the flavours are given the chance to mix and mingle, even for a few hours. Make it up to 2 days in advance and store in a covered container in the fridge. Garnish with olive oil and fresh thyme just before serving.)