Place garlic heats cut-side down in a baking dish and cover with olive oil. Place thyme in oil. Cover with aluminum foil, then place the dish on a baking sheet. Roast for 45 minutes. Using kitchen tongs, remove garlic and place on a paper towel to drain. Pour olive oil through a fine mesh strainer and keep in a seal tight container or jar. It should last about a month.
After the garlic has cooled, squeeze the cloves out of each bulb. Keep them whole or mash them with a fork, using as desired.