Defrost the puff pastry sheet and heat your oven to 425 degrees.
Peel and core the apples. Slice them very thinly.
Pour the brown sugar, butter, flour, vanilla, and salt into a bowl and use a fork to combine, mixing it into small crumbs. Add the apples and coat them in the crumbs.
Press the puff pastry into a tart pan, stretching it slightly to fit, and lightly pressing the dough up the sides of the pan.
Arrange the apples in the tart pan, fanning then out closely in layers.
Bake for 18-20 minutes, until the puff pastry is golden brown and puffy.