1. Preheat oven to 205°C (400°F).
2. Rinse snails in cold water and drain.
3. Heat oil in a skillet over medium heat. Cook snails, shallots and mushrooms for 5 to 7 minutes.
4. Add white wine and season with salt and pepper. Continue cooking for 2 to 3 minutes, until all liquid has evaporated. Remove from heat and let cool.
5. In a bowl, mix snail mixture with cheese and parsley.
6. Brush phyllo sheets with butter and layer as you go. Cut sheets into 12 equal squares.
7. In the center of each square, place 22.5 ml (1 ½ tbsp.) of snail mixture. Close by bringing the dough over the filling.
8. On a baking sheet lined with parchment paper, place the bundles. Bake for 12 to 15 minutes, until golden brown.
9. Meanwhile, combine wine for sauce with shallots in a saucepan. Bring to a boil, then simmer over low-medium heat until all liquid has evaporated.
10. Add the cream, Parmesan and Espelette pepper to the pan and stir. Simmer for 4 to 5 minutes over low heat.
11. Serve the bundles with the sauce.