Heat the olive oil in a sauté pan, or in an earthenware dish set on a heat-diffusing mat. Put in the tomatoes, garlic and shallot, cover, and cook for about 15 minutes. Uncover, and let much of the liquid evaporate for about 5 minutes.
Having cracked each egg into a saucer, slide them, one by one, into the tomato mixture. Cook for 3 to 4 minutes more, until the eggs are set.