Preheat the oven to 400 degrees F (200 degrees C). Grease 12 small (3 1/2-inch) fluted brioche pans.
Sift flour, sugar, baking powder, and salt together in a mixing bowl. Add butter and cold water; mix until dough forms into a ball.
Roll dough on a lightly floured work surface with a lightly floured rolling pin to 1/8-inch thickness. Cut dough into rounds and press lightly into the prepared pans.
Mix hot water and sugar in a bowl until sugar melts. Whisk in eggs; pour in evaporated milk and vanilla extract and mix well. Divide egg mixture between dough shells.
Bake in the preheated oven until egg is almost firm in the middle, 14 to 16 minutes. Let cool 10 minutes before transferring to a wire rack.
