Preheat oven to 550 degrees.
Lightly grease the muffin tins with the butter.
Add the sugar, water, sliced lemon zest, and vanilla to a small saucepan and bring to a boil without stirring.
Remove from heat when the temperature reaches 210 degrees Fahrenheit.
In another cold saucepan, combine the milk, sifted flour, and salt and whisk.
Cook over medium heat for around 5 minutes, constantly whisking, until well combined and thickened.
Remove from heat and allow to cool for 10 minutes.
Once the milk mixture has cooled, whisk in the egg yolks until well combined.
Remove the cinnamon stick from the sugar syrup and pour it into the milk mixture.
Mix until well combined.
Strain the mixture into a pourable bowl or cup.
Roll the puff pastry sheet thinner on a cutting board.
Score the pastry into 12 even pieces.
Place one square into each greased muffin tin.
Dip your fingers in the bowl of cold water to mold the pastry into shape so the top is 1/8 inch over the edge of the muffin tin.
Fill each pastry cup 3/4 full with the custard filling.
Bake at 550 degrees until the pastry is golden brown and the custard is caramelized and blistered, about 10 to 12 minutes.
Let the tarts cool in the muffin pan for 5 to 10 minutes.
Remove the tarts carefully and, if desired, dust with cinnamon and powdered sugar.
Serve while still warm.
