Heat the oil in a small heavy frying pan and add the tomatoes, sugar, garlic and fines herbes. Cook over a moderate heat, stirring, until the tomato juices have evaporated. Remove and discard the garlic then season the tomatoes.
Pour the eggs over the tomatoes , then lower the heat and cook very gently, stirring occasionally with a wooden spoon until the eggs have formed soft curds.
When the eggs are almost done add the basil, then remove from the heat and stir in the butter, cut up small.