Preheat the oven to 350 degrees and line 2 baking sheets with parchment paper.
To make the filling, pulse the spinach, egg, and feta in a food processor just until the spinach is chopped and the cheese mixed in. Add freshly ground black pepper to taste. Set aside.
Cut the fillo lengthwise into 3 strips and cover with a moist towel to prevent breaking. Take one strip and butter with a pastry brush. Place about 2 teaspoons of filling at the bottom of the strip. Fold to make a triangle and continue folding until the end of the strip (like you fold a flag). Place completed triangle on the prepared baking sheets.
Repeat with the remaining fillo strips, using the rest of the filling. Reserve any leftover fillo for another use.
Brush the top of each triangle with the egg wash and sprinkle with sesame and nigella seeds. Bake for 20 to 25 minutes, until golden brown.