Meanwhile, add milk, caster sugar, and butter to a saucepan. Cook the mixture over medium heat, stirring constantly until the butter has melted. Bring the mixture to a simmer, then reduce the heat to medium-low and add flour all at once. Keep stirring the mixture until the flour is well incorporated and smooth.
Turn off the heat, and transfer the mixture to a clean mixing bowl. Let the mixture cool for 3 to 5 minutes, then slowly whisk in the beaten egg little by little. Once the mixture becomes thick, shiny, and smooth, stop whisking and transfer it to a piping bag using a spatula.
Preheat the oven to 200°C (410°F).
While preheating the oven, remove the pastry (cookie-like) dough from the refrigerator and roll it out to about 2 mm (2/25 inches) thick. Cut the dough with a 2-inch (5 cm) diameter round cookie cutter.
Line a baking pan with parchment paper, and pipe 2-inch (5 cm) mounds onto the paper, about 3 inches (7 cm) apart. Top each mound with the cookie-like pastry dough.
Bake the pastries for 10 minutes, then reduce the oven temperature to 160°C (320°F) and continue baking for 20 minutes until golden brown and crispy. Once the pastries are baked, remove them from the oven and transfer them to a cooling rack.