Remove and discard the artichoke stems. Peel off lower leaves (approximately 18.) Slice off the top half so that only the light green remains (artichokes should be approximately 1 1/4 inches), then cut the artichoke in half lengthwise.
Place the artichokes in a medium pot, flat side down, and add olive oil to just cover.
Add the garlic, thyme, salt and pepper. Bring the olive oil to a boil, cover the pot and reduce the heat to a low flame and simmer for 15 minutes. Insert a knife into the lower half and if easily penetrated, it's done.
Remove the thyme and garlic from the pot, raise the heat and fry uncovered for approximately 2 minutes, turning over the artichokes midway. They are done when brown and crispy.
Remove the artichokes from the pot and place them on paper towels flat side down.