Preheat the oven to 400°.
Grease a small dish with oil.
Wash and dry the tomatoes.
Cut a cap off the top, hollow out, and sprinkle the insides with the salt and pepper.
Wash and pat the tarragon dry, chop 12 leaves and sprinkle inside the tomatoes.
Beat the eggs one after another and pour one into each tomato.
Sprinkle Parmesan on top.
Set the tomatoes in the baking dish.
Bake 15 minutes, covering with aluminum foil after 10 minutes if needed.