Make the doughnuts: Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Unfold one puff pastry sheet on a work surface and brush off the excess flour. Brush all over with the beaten egg. Unfold the second puff pastry sheet on top of the first one and press to seal. Cut out eight rounds using a 3-inch cookie cutter. Cut out the middles with a 1-inch cookie cutter. Cut out more 1-inch rounds from the scraps, if desired. Arrange on the prepared baking sheet and bake until browned and crisp, 20 to 25 minutes.
Microwave the peach preserves until melted, about 30 seconds. Brush on the doughnuts and doughnut holes while still hot. Let cool completely on the baking sheet.
Meanwhile, make the filling: Combine the peaches, peach nectar and salt in a small saucepan. Cook over medium heat, stirring occasionally, until the peaches are soft and most of the liquid has evaporated, 8 to 10 minutes. Transfer to a blender and puree until smooth. Refrigerate until thick and cold, at least 2 hours.
Make the glaze: Whisk the confectioners' sugar, 1 tablespoon peach nectar, the lemon juice and vanilla in a small bowl until smooth; add up to 1 more tablespoon peach nectar if needed.
Using a sharp knife, cut each doughnut horizontally into 3 rings. Spread some of the peach filling on the bottom rings and top with a second ring, then spread with more peach filling and add the top ring. (You will not use all the filling.) Drizzle the glaze over the doughnuts. Sprinkle with the freeze-dried strawberries. Let the glaze set, 10 to 15 minutes. Serve at room temperature or chilled with the remaining peach filling for dipping.