Preheat oven to 200C. Roll out pastry to 3mm thick, place on a tray and refrigerate to rest (30 minutes).
Meanwhile, for cinnamon-verjuice syrup, stir ingredients and 80ml water in a saucepan over medium-high heat until sugar dissolves, bring to the boil and cook until a light syrup forms (10-15 minutes). Remove from heat and set aside.
Cut out a 23cm-diameter round from pastry, place on an oven tray lined with baking paper and set aside. Rub sugar, vanilla seeds and cinnamon in a bowl to combine, then pass through a sieve and set aside. Trim ends from apples, thinly slice on a mandolin (discard seeds), then layer over pastry in concentric circles, leaving a 1cm border. Brush apples with half the butter, then scatter half the sugar mixture evenly over and bake until starting to puff and turn golden (10-15 minutes). Remove from oven and brush with remaining butter, scatter with remaining sugar, then return to oven until dark golden and cooked through (20-25 minutes; cover edges of pastry with foil if they start to darken too much). Serve warm drizzled with cinnamon-verjuice syrup and with crème fraîche.
