Cut the tops off the garlic bulbs, place on a clean working surface, and press down firmly with the flat part of a large knife to separate the cloves from the bulb. Remove the skins and discard.

Pour oil into a very small pot; add garlic cloves and thyme.

Turn heat to medium and cook until bubbles start to form. Lower the heat to the lowest possible setting and cook until garlic is soft but not brown, 20 to 25 minutes, depending on the size of the cloves.

Place garlic cloves and oil in an ice cube tray and freeze until firm, 2 to 3 hours. Remove frozen cubes from the tray and store in a freezer bag.