In a medium bowl, whisk together egg, parsley, garlic and chilli flakes. Mix in Gouda and Emmentaler.
One sheet at a time, place filo pastry on a flat surface and brush with about 1 tablespoon butter. Cut lengthwise into 4 strips. Place a rounded teaspoon of the egg mixture at one end of each strip. Fold corner of strip over the filling, forming a triangular fold. Continue folding the length of the strip in triangular folds to form a small stuffed triangle. Repeat with remaining filo.
Preheat oven to 180 degrees C. Lightly butter a large baking sheet.
Arrange stuffed filo triangles in a single layer on the prepared baking sheet. Bake in the preheated oven 30 minutes, or until lightly browned. Serve warm.