Preheat the oven to 500°F with a rack in the upper third. Lightly grease a 12-cup muffin tin with oil.
On a lightly floured surface, roll the puff pastry into a 10x12-inch rectangle. Starting from a short side, roll it up tightly into a log and cut it into 12 equal rounds.Place each round cut side up in a muffin cup. Dip your thumbs in cold water and press down on the center, pushing the dough up the sides until it reaches just above the rim, then chill the tin for 15 minutes.
Combine the sugar, water, cinnamon stick and lemon peel in a small saucepan and bring to a boil. Simmer for 3 minutes, then remove from the heat and discard the cinnamon stick and lemon peel.
In a separate saucepan, whisk the oat milk, coconut milk, flour and salt until smooth. Cook over medium heat, whisking constantly, for 3-4 minutes until it thickens to a thin pudding consistency, then remove from the heat.
Slowly whisk the warm syrup into the milk mixture, then stir in the vanilla. Let it cool for 10 minutes until warm but not hot.Whisk in the egg yolks until smooth, then strain the custard through a fine mesh sieve into a measuring cup with a spout.
Pour the custard into the chilled pastry cups, filling each one about 3/4 full. Bake for 12-16 minutes, until the pastry is deep golden and crisp and the custard is puffed with dark caramelized spots on top.
Let the tarts cool in the pan for 10 minutes, then transfer them to a wire rack. Dust with powdered sugar and cinnamon and serve warm or at room temperature.