Heat a large skillet over medium heat. Add the pre-cooked gyro slices in a single layer and cook for about 1–2 minutes per side until lightly browned and heated through.
Transfer the gyro slices to a cutting board and cut each slice in half. Let them cool slightly before assembling — this makes wrapping much easier and prevents the wrappers from softening.
Pat the tomato slivers gently with a paper towel to remove excess moisture.
Lay one egg roll wrapper flat on a clean surface in a rectangular position.
Arrange a few pieces of the halved gyro meat in a neat line toward one side of the wrapper, leaving the left and right edges clear.
Add a small handful of tomato slivers and red onion strips directly on top of the meat.
Spoon some tzatziki dressing over the tomato and onion layer, then sprinkle with crumbled feta and chopped parsley. Keep everything in a tight line.
Fold the left and right sides inward over the filling.
Starting from the side closest to the filling, roll the wrapper up tightly into a log shape.
Brush a small amount of water along the final edge of the wrapper and press firmly to seal. Repeat with remaining wrappers and filling.
Heat about 1 to 2 inches of neutral oil in a heavy-bottomed pot to 350°F. Fry egg rolls in batches for 4 to 5 minutes total, turning occasionally, until golden brown and crispy.
Transfer to a paper towel-lined plate to drain.
Serve warm with extra tzatziki dressing for dipping.