1. Preheat the oven to 175°C (350°F) and line a baking sheet with parchment paper.

2. In a large mixing bowl, combine 250g (2 1/4 cups) of flour, 6g (1 teaspoon) of salt, and 2g (1/2 teaspoon) of cayenne pepper. Add 115g (1/2 cup) of softened butter and mix until the dough comes together.

3. Gradually add 60ml (2 fluid ounces) of water while mixing until a smooth dough forms.

4. Divide the dough into two equal parts. On a lightly floured surface, roll out each half into a thin sheet, about 3mm (1/8 inch) thick.

5. Spread half of the 60g (1/2 cup) shredded Parmesan cheese on one sheet, leaving a 2.5cm (1-inch) border around the edges. Top with 60g (1/2 cup) shredded aged cheddar cheese.

6. Place the second sheet of dough on top and press the edges to seal. Cut into desired shapes using a cookie cutter or a knife.

7. Place the pastry bites on the prepared baking sheet, leaving about 2.5cm (1 inch) of space between each piece.

8. Brush the tops with a beaten egg and sprinkle with the remaining 30g (1/4 cup) Parmesan cheese and 55g (1/2 cup) aged cheddar cheese.

9. Bake for 20-25 minutes or until golden brown.

10. Allow the pastry bites to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.