Preheat oven to 500 °F (260 °C) or as high as your oven allows for best caramelization.

Prepare pastry shells: Roll out puff pastry to about ⅛‑inch thick, roll into a tight log, then slice into rounds and press each round into a muffin or tart tin to form thin-walled cups. Chill while preparing custard

Make custard: In a saucepan, combine sugar with water and cinnamon stick; simmer until syrupy, then remove cinnamon. Whisk egg yolks and whole egg together. Slowly whisk in hot milk (or cream) and vanilla into eggs. Return to low heat and whisk until thickened, or stir in cornstarch if using to achieve custard consistency. Chill custard fully before filling.

Fill and bake: Pour chilled custard into pastry cups nearly to the rim. Bake at high heat for about 12–15 minutes, until pastry edges are puffed and custard surface develops signature dark spots or caramelized spots

Let tarts rest briefly, dust with powdered sugar and cinnamon if desired, and serve warm.