Peel the apples and chop them finely, keeping the skin on. Season with lemon juice and set aside.
Thinly slice Fontina PDO, removing the rind, and set aside.
Unroll the puff pastry on a baking tray and divide it into 6 parts with the help of a pastry wheel. Pierce the base with a fork leaving a one cm border and place the slices of Fontina PDO in the middle. Lay the apple slices on top and season with a pinch of black pepper, some fresh thyme, a pinch of salt and brown sugar.
Brush the edges with beaten egg yolk and bake in a preheated oven at 200° C for 10/15 minutes.
Slice Fontina PDO into sticks, removing the rind. Place them well apart on the silicone mat-covered microwave tray.