Heat 2 tablespoons of butter in a large skillet over medium-high heat until sizzling. Add the apples and toss to coat. Saute until a lot of the moisture from the apples has evaporated and the apples just start to soften and turn brown, 8 to 10 minutes. Add the honey, ginger, cinnamon, and salt and toss to blend. Taste and add more of any of these flavorings, if desired. Set aside to cool.
On a lightly floured work surface, roll the pastry into a 10-by-15-inch rectangle. Cut into six 5-by-5-inch squares, then trim the corners of each square to make a rough round.
Heat the oven to 400°F (200°C).
Arrange the pastry rounds on a baking sheet and prick each one at 1/2-inch intervals. Divide the apple filling evenly among the pastry rounds, leaving about a 1/2-inch border of pastry.
Wet the border with a little water and loosely pleat it to create an edge that embraces the apples. The pastry shouldn't cover the center of the apple filling. Brush the edge of the pastry with some melted butter.
Bake the tarts until the pastry is pale gold and set, about 18 minutes. Brush a little more butter onto the pastry and continue baking until the pastry is puffed and a rich golden brown on the border and undersides, another 5 to 7 minutes.
Slide the tarts onto a cooling rack. Sprinkle each one with a heaping tablespoon cinnamon-sugar walnuts and let cool for at least 15 minutes or up to 1 hour before serving.