Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Put the spinach in a kitchen towel and wring very dry (to get about 1/2 cup dry spinach). Put the spinach into a large bowl, breaking up the clumps with your fingers. Add the cream cheese, feta, scallions, dill, Parmesan, lemon zest, 1/2 teaspoon salt and some black pepper. Mix well.
Lightly flour your hands and work surface. Unroll the crescent dough and separate into triangles along the perforated lines. Put about a tablespoon of filling at the shortest end of a triangle, and roll. Place the roll, point-side down, on the prepared baking sheet, tucking in the ends to form a crescent shape. Repeat with the remaining triangles and filling, spacing the rolls at least 1 inch apart on the baking sheet.
Brush the dough with the egg wash and bake until puffed and golden brown, about 12 minutes. Let the crescents cool on the baking sheet for a few minutes before transferring to a cooling rack. Serve warm or at room temperature.