Heat butter in a saucepan over medium heat. Slowly cook and stir onion until tender, approx. 5 minutes. Combine with spinach. Stir in feta cheese, cottage cheese and egg. Cook and stir until thick (approx. 5 minutes). Reduce heat and let simmer. Preheat oven to 400 degrees.
Unroll phyllo dough sheets one sheet at a time on flat surface. Brush with unsalted butter. Cut into strips about 5 inches wide. Place 1 tablespoon of the onion, spinach and feta mixture at one end of each dough strip. Fold the end of the strip over the filling so that it forms a triangle. Continue folding the strip in triangles until a small, triangular stuffed pastry remains. Brush with unsalted butter. Repeat with process until all of the phyllo dough is used.
Place stuffed triangles on baking sheet. Bake in the oven 12 - 15 minutes, or until golden brown. Remove from oven, let cool for 5 min and serve warm.