Fill a medium saucepan with enough hot water to cover the eggs. Bring the water (without the eggs) to a gentle boil. Lower the eggs cautiously into the water with a slotted spoon. When the water boils again, lower the heat so the water is just simmering, and cook for 4 minutes.
While the eggs are cooking, puree the artichokes and goat cheese in a food processor until smooth. (This can also be used as a spread or dip for a quick appetiser, it will keep for a few days).
Slice the baguette horizontally as you would for a sandwich. Toast it and spread with the artichoke mixture. Cut into fingers, thin enough to be easily inserted into the egg. Sprinkle with thyme and pepper.
Drain the eggs and sit them snugly in eggcups (shot or cordial glasses work well too). Serve with the bread fingers.