Cook greens in batches in a large pot of boiling water until tender, 1 to 2 minutes, and transfer batches to a bowl of ice water.
Preheat oven to 375°. Drain greens and squeeze as dry as possible. In a bowl, stir greens with oil, salt, and pepper.
Butter an 8-in. square baking pan and lay 1 filo square in bottom. Brush lightly with butter and top with 5 more squares, buttering each. Top with greens, then cheese. Repeat filo layering and buttering with remaining sheets, then cut through all the layers into 9 pieces. Bake until golden and crisp, about 55 minutes.
*Or use 3 bags (10 oz. each) chopped mustard greens; they'll be slightly chewier, since the ribs are included.