1. Preheat the oven to 210°C (410°F).
2. Thoroughly wash the potatoes without peeling them.
3. In a large pot, cook them in boiling salted water for 15 minutes.
4. Drain them and cut them in half.
5. Soften the butter.
6. In a bowl, mix together the softened butter, egg, cheese, cream, and thyme leaves.
7. Hollow out the potatoes and incorporate their flesh into the previous mixture.
8. Stuff the potatoes with this mixture.
9. Grease a gratin dish.
10. Arrange the potatoes in the dish and drizzle with a little olive oil.
11. Bake in the oven for 15 minutes.