Make the shoestring fries
Peel the russet potato and cut into matchsticks using a julienne peeler or mandoline fitted with a julienne blade. If you do not have a julienne peeler, slice the potatoes into ¼-inch slabs lengthwise and then cut into the thinnest fries you can. Add to a bowl of cold water and set aside.
Bread the cutlets
Combine the flour with 1 teaspoon salt in a shallow baking dish. In another dish, beat the eggs with ½ teaspoon salt. In a third bowl, combine the panko, paprika, and the remaining ½ teaspoon salt and toss to coat. Season each cutlet generously with salt, then dip each piece of chicken in the flour, shaking off the excess. Dip into the egg mixture, letting the excess drip off, then press firmly into the panko mixture on both sides. Let the breaded cutlets sit out while you make the dressing—this helps the breading stick better when fried.
Make the dressing
Whisk all the dressing ingredients together in a bowl and set aside.
Fry the cutlets
Heat ½ inch of oil in a very large skillet over medium heat. Test the oil by dropping in a panko crumb—if it sizzles and turns golden immediately, it’s ready. Working in two batches, gently lay the cutlets in the oil (away from you) and fry until golden and crisp, 2–3 minutes per side. Transfer to a wire rack set over a sheet pan to drain, cool slightly, then cut into 1-inch strips.
Fry the shoestrings
Drain the shoestring fries and dry thoroughly. Fry the potatoes in batches for 1–2 minutes, until golden brown (they cook fast, so watch closely). Transfer to a wire rack set over a sheet pan to drain and immediately season generously with salt. If using frozen fries, bake according to package instructions, adding a few extra minutes until extra crispy.
Assemble the salad
Arrange the lettuce on a large platter. Top with the cutlet strips and avocado slices, drizzle with half the dressing, then finish with the shoestring fries and parsley. Season with more salt and pepper and serve with extra dressing.