Preheat the oil in a deep fryer (or a large, heavy-based pot) to 350 degrees F.
Wipe the tops of the mushrooms with a damp cloth to clean, and then scrape the gills off from the underside with the back of a spoon. Trim the stem and slice into 1/4-inch strips.
Place the flour into a rimmed dish, the beaten eggs in a second rimmed dish and sprinkle both with some salt and pepper. In a third dish add the panko, some Italian seasoning, the paprika, garlic powder, and some more salt and pepper. Mix well. Dredge the mushroom "fries" in the flour, followed by the egg mixture and finally in the seasoned panko.
Working in batches of 5 to 6, fry the mushrooms in the hot oil until golden brown and crunchy, about 4 minutes. Drain on a wire rack over some paper towels and season once more with salt.