Unroll phyllo dough; cover with plastic wrap. Remove one sheet and place on cutting board or flat surface; brush with margarine or butter. (Keep remaining phyllo covered while working.) Arrange one-third of parsley in single layer over phyllo. Place another phyllo sheet on top of the first; brush with some of the butter. Cut phyllo in half crosswise.
Lay one-sixth of carrot strips, end to end, along the edge of one 12-inch side of phyllo; sprinkle with one-sixth of onion. Starting with the 12-inch side with carrots, roll up phyllo. Cut the phyllo roll into 4 diagonal pieces, each about 3 inches long. Repeat with remaining phyllo.
Repeat process with remaining 4 sheets of phyllo, butter, parsley, carrot, and green onion, making 24 wraps total. Brush any remaining butter on top of appetizers.
Place on cookie sheet. Bake in 375 degree F oven for 11 to 13 minutes or until golden brown. Transfer to clean white paper towels; let stand 1 minute. Serve warm. Or, cool on wire rack. Makes 24 appetizer servings.