This recipe has been altered from the original recipe to make it less time consuming. The apple juices will run onto the paper during baking but the bottom of your tart should be fine. Do use parchment paper to protect the tarts. These are delicious. It looks like a treat from the bakery! I do believe that if you place the tarts directly on a baking rack large enough to fit over the parchment covered sheet pan before baking it will also protect any "juice" browning on bottom.
Preheat oven to 400 degrees. Core apples and remove stems; half the apples and slice crosswise into 1/4 inch, thin slices. Cover the bottom of a rimmed baking sheet with parchment paper.
Lay out Puff Pastry on a floured dough cloth. Cut both sheets into fourths so you have 8 squares. Place overlapping slices of apples on each square (approximately 8 slices per square); generously sprinkle the sugar on top of the apples. Dot each apple tart with the cubed butter.
Bake at 400 degrees for approximately 40 minutes (or until edges of apples and pastry start to brown) turning the pan halfway through baking. When the tarts are done heat together the apricot preserves, water and the orange liqueur. Brush each tart completely with the preserve mixture. Add chopped walnuts. Let cool or serve warm.