Thaw the frozen puff pastry at room temperature for about 45 minutes or until it’s soft and easy to handle.
Place the dried mushrooms in a medium bowl and the chile pepper in a small bowl. Cover both with boiling water. If the chile floats, place something heavy on top to keep it submerged.
Allow the mushrooms and chile to rehydrate for 30 minutes, then drain the water.
Place the mushrooms on a double layer of paper towels and roll it up to extract as much water as possible. Split the chile lengthwise and remove the stem and seeds.
Finely chop the chile and mushrooms.
Heat a medium sauté pan over medium heat. Once hot, add the olive oil.
Add the shallots and garlic, then sauté until soft, about 5 minutes.
Add the mushrooms and chile, then cook until the mushrooms are soft, about 5 more minutes. Season with salt and pepper and remove from heat.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Place the pastry on a lightly-floured surface. Use a rolling pin to smooth out the pastry and get rid of any folds.
In a small bowl, combine the egg substitute and water. Brush a thin layer of the egg mixture on top of the pastry.
Spread the mushroom mixture onto the pastry, stopping a ½-inch away from the edges.
Reserve about 2 tablespoons of the cheese, then sprinkle the rest on top of the mushrooms.
Roll up the pastry, jelly-roll style, then brush the seam with the egg mixture.
Using a serrated knife, slice the roll into ½-inch wide slices. You should end up with about 16 pieces. Place the slices, cut-side down, on the prepared baking sheet.
Brush with the egg mixture, sprinkle with the remaining cheese, then place in the oven and bake for 15-17 minutes or until the pastry is golden brown.