Peel the eggs and set them aside.
In a saucepan, melt the butter, add the flour, and whisk until the mixture is foamy.
Gradually add the milk, whisking constantly.
Let it boil for a few minutes, stirring constantly.
Season with salt, pepper, and nutmeg.
Saute the onion in oil, add the diced tomatoes, and cook for 5 minutes, stirring occasionally.
Add the vinegar and tomato paste, and cook for another 5 minutes.
Preheat the oven to 425 F (220 C).
Mix the bechamel sauce with the tomato sauce.
Pour half of the mixture into 4 gratin dishes.
Place 4 egg halves in each dish and cover with the remaining sauce.
Sprinkle the dishes with grated cheese and butter bits.
Bake for 20 minutes or until the dishes are golden brown.