Combine the flour and a pinch of salt in a large bowl. Add the cold butter and use your fingers or a pastry cutter to work it into the flour until the mixture resembles coarse crumbs.
Gradually add the cold water, a little at a time, mixing gently until the dough just comes together. Knead lightly on a floured surface for about 30 seconds to smooth it out, then wrap in plastic wrap and chill in the fridge for 15 minutes.
While the dough chills, grate the sharp cheddar cheese and chop the fresh parsley. Mix them together in a small bowl and set aside — this will be your filling.
Preheat your oven to 200°C (390°F) and line a baking sheet with parchment paper. Remove the dough from the fridge and roll it out on a floured surface into a rectangle about 30x20 cm (12x8 inches), roughly 3 mm thick.
Spread the softened butter evenly over the surface of the dough, then sprinkle the cheese and herb mixture over the butter, pressing lightly to help it adhere.
Starting from one long edge, tightly roll the dough into a log, keeping it as even as possible to create a neat spiral.
Use a sharp knife or pizza cutter to slice the rolled dough into 1.5 cm (0.6 inch) thick pinwheels. Place them cut-side up on the prepared baking sheet, spacing them about 2 cm apart.
Brush the tops of each pinwheel with the beaten egg for a shiny, golden crust. Bake in the preheated oven for 15-18 minutes, or until the edges are crisp and golden, and the cheese is bubbly.
Remove the pinwheels from the oven and let them rest for about 5 minutes. Serve warm or at room temperature, enjoying the crispy exterior and gooey cheese inside.
