Heat oven to 375°F. Lightly grease cookie sheets, or spray with cooking spray. In food processor bowl with metal blade or blender container, place olives, oil and garlic powder. Cover and process with on/off pulses until finely chopped.
If using crescent rolls: Unroll dough and separate dough into 4 rectangles. Press each to form 7x4-inch rectangle; press perforations to seal. If using dough sheet: Unroll dough and cut into 4 rectangles. Press each to form 7x4-inch rectangle.
Brush dough rectangles with beaten egg. Evenly spread olive mixture on 2 of the rectangles. Top with remaining 2 rectangles, egg-brushed side down; press down. With thin sharp knife, cut each filled rectangle crosswise into 8 strips. Place strips 1 inch apart on cookie sheets, twisting each 2 or 3 times. Brush tops of strips with beaten egg. Sprinkle strips lightly with cheese.
Bake 10 to 13 minutes or until golden brown. Serve warm or cool.