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Line a baking sheet with parchment paper. In a small bowl, beat 1 egg. Lightly sprinkle counter with flour and place 1 piece of pastry on top. Dust rolling pin with flour. Roll pastry into a square, about 10-x 10-in. (25-x 25-cm). While rolling out, if sticking, sprinkle a little flour on the counter. Turn pastry a few times. Cut into four 5-x5-in. (12.5-x 12.5-cm) squares. Repeat with remaining piece of pastry.
In a large bowl, beat remaining eggs. Crumble in the cheeses, stirring well to combine. Place one square on a cutting board. Brush edges of square with beaten egg. Place 2 tbsp (30 mL) cheese mixture in centre of square. Pick up 1 corner and fold it over the opposite corner to form a triangle. With a fork, press the edges tightly together to seal. Repeat with remaining squares and cheese mixture. Brush tops of triangles with beaten egg. Place on prepared baking sheet. Refrigerate at least 20 min.
When ready to bake, preheat oven to 400F (200C). Bake in centre of oven for 10 min. Then reduce heat to 350F (180C). Continue to bake until golden brown, from 15 to 20 more min. Serve hot or at room temperature.