Combine cheese, eggs, parsley and salt and mix well. Cut each sheet of phyllo dough in halves, working with one sheet at a time. Keep rest of pastry covered with damp towel until ready to use.
Brush with butter and fold each half twice vertically to form narrow strip. Place about 1 tablespoon cheese mixture at one end of each strip.
Fold one corner across filling to form triangle. Brush with more butter. Continue folding in triangles, flag-style, and brushing with butter. Place triangles on baking sheets and bake at 350F until pastry is golden, about 15 to 20 minutes.