Start by boiling the lentils in salted water until they’re tender but still firm. Drain and set them aside. These form the base texture of your filling, so don’t overcook them.
In a large pan, heat the vegan butter over medium heat. Add minced garlic and sage, and cook until fragrant. Toss in the chopped onion and sauté until golden and soft. Stir in the mushrooms and cook until all the liquid has evaporated. Add lentils, chestnuts, rosemary, soy sauce, and pepper, and stir well to combine. Remove from heat and let it cool slightly.
Preheat your oven to 400°F (200°C). On a lightly floured surface, roll out the puff pastry into a large rectangle. Spoon the filling down the center third of the pastry, shaping it into a log. Cut diagonal strips along the sides of the pastry and fold them over the filling in a crisscross pattern.
Mix the aquafaba with soy milk and brush it generously over the pastry. Place it on a parchment-lined tray and bake for 25–30 minutes until golden brown. Let it rest for a few minutes before slicing and serving.