Sauté the onion in the oil for 5 minutes in a medium skillet. Add the spinach. Simmer the mixture over medium-low heat, stirring occasionally until most of moisture is evaporated.
Crumble the feta cheese into small pieces. Add the cottage cheese and eggs; mix well. Toss the bread crumbs into the spinach mixture and add to the cheese mixture. Stir until blended.
Carefully cut the phyllo sheets into thirds. Refrigerate two of the three segments until needed and cover the remaining sheets with a slightly damp towel. Remove 1 sheet of phyllo pastry and fold in half lengthwise. Brush the pastry with the melted butter. Place 1 tablespoon of the spinach filling near the end. Fold the pastry over in a triangle shape.
Continue folding the pastry like a flag, keeping the triangular shape. Lightly butter the top. Repeat the process with remaining pastry and filling. Bake in a 425 degree
oven for 20 minutes or until golden brown. Serve warm.