To make the sauce, melt the butter in a saucepan and add the flour.
Stir for a minute over medium heat then slowly whisk in the milk. The sauce needs to be very thick (but still creamy) in consistency so you might not need all the milk.
When the sauce is smooth, creamy and thick, turn the heat down and cook the sauce out for approximately 7-10 minutes, stirring regularly, until the sauce is velvety smooth and all flouriness has been cooked out.
When the sauce is cooked, remove from the heat then add the cheese, steamed broccoli, cayenne pepper and seasoning and stir to combine. Cover the surface of the sauce with a piece of plastic wrap to prevent a film from forming then set aside.
Pre-heat the oven to 180°c.
Place the pastries in the holes of a shallow muffin tin, pressing down properly.
Spoon in the broccoli filling then fold over the edges of the pastry.
Brush with the beaten egg and place in the oven.
Allow the pastries to bake for 20-25 minutes until they pastry is golden, crisp and cooked through.
Remove from the oven and allow to rest for 10 minutes before serving.