Place the oven rack in the lower third of the oven and preheat the oven to 400° F/200° C.
Halve the leeks lengthwise and wash well. Soak in a bowl of cold water for about 5 minutes to float away any remaining dirt. Drain well and thinly slice. Place slices in the colander and allow to finish draining with the asparagus pieces.
In the medium bowl, whisk together the eggs, feta cheese, parsley, and black pepper. Stir in the drained leeks and asparagus until evenly distributed.
Place one piece of the fillo dough in the baking dish and brush with melted butter. Repeat with 9 more pieces of fillo. Pour in the leeks and asparagus mixture and spread to fill the dish. Place the remaining layers of fillo on top, brushing with melted butter between the layers. Tuck in the edges or trim as necessary.
Bake in the preheated oven until the top is golden brown and crispy and the middle is bubbly, about 30 minutes.