Roll the puff pastry into a tight log from one long side and chill it for 20 minutes. Grease a 12-cup muffin pan with the softened butter.
Divide the chilled pastry log into 12 equal pieces. Place one piece cut-side down in each muffin cup, then press the pastry across the bottom and up the sides with slightly damp fingertips. Chill while the custard is prepared.
Whisk 1/2 cup of the whole milk with the cornstarch and all-purpose flour until smooth. Add the remaining milk, heavy cream, granulated sugar, ground cinnamon, lemon zest, and fine salt.
Cook the custard over medium heat, whisking constantly, until it thickens and just begins to bubble. Cook for 30 seconds more, then remove from the heat and whisk in the butter and vanilla extract.
Heat the oven to 475°F. Divide the warm custard among the pastry shells, filling each about three quarters full.
Bake for 13 to 16 minutes until the pastry is deeply golden and the custard tops have browned spots. Cool in the pan for 10 minutes, then transfer the tarts to a rack.
Serve slightly warm or at room temperature. For the crispest shells, avoid refrigerating the tarts until they are completely cool.
