Heat 1 tablespoon of oil in medium skillet over medium heat. Add white and green chopped onions; cook until softened, 3 to 4 minutes.
Meanwhile, mix spinach, feta, cottage cheese and egg in medium bowl. Add cooked onions and season with salt, and pepper. Cover and refrigerate until ready to use.
Combine the remaining butter and oil and set aside until ready to use.
Remove one phyllo sheet. With the shortest end of the phyllo sheet nearest you, brush phyllo with butter and oil mixture; top with second sheet and brush again. Fold the buttered phyllo sheets in half, like a book and brush the top layer with butter and oil mixture.
Place a heaping 1-1/2 tablespoons of filling in the center of the bottom nearest you. Fold up the phyllo once and then fold over the right side and then the left side of the phyllo. Brush with butter and oil mixture and then continue rolling up like a burrito.
Place seam side down on a greased baking sheet and brush rolls with butter/oil mixture. Bake until golden, about 30 to 35 minutes.