Peel off loose outer cabbage leaves. Cut in half through root, then cut each half into 2 equal wedges. Cut 2 (1/2"-thick) cutlets from each wedge (for a total of 8), making sure each has some root stem attached to hold it together. (There will be a side wedge of disconnected cabbage leftover from each larger wedge; reserve for another use.)
Preheat oven to 200°. Line a baking sheet with parchment. Place a wire rack inside another baking sheet.
Place flour in a wide shallow dish. In a second shallow dish, beat eggs and mustard until blended. In a third shallow dish, combine panko, pepper, and 1/2 teaspoon salt.
Season cabbage cutlets on both sides with 2 teaspoons salt. Working one at a time, coat cutlet in flour, then dip into egg mixture, rubbing all over cabbage to fully coat. Dredge in panko mixture, firmly pressing to adhere. Place breaded schnitzels on parchment-lined sheet.
Into a large, heavy pan, pour oil to a depth of 1/4". Heat over medium-high heat until a deep-fry or instant-read thermometer registers 350°. (A bread crumb dropped into oil should immediately sizzle.)
Working in batches, fry breaded schnitzels until golden brown on the bottom, 2 to 3 minutes. Carefully flip and fry, basting any pale patches with a spoonful of oil, until golden brown on the other side, 1 to 2 minutes more. Transfer to prepared rack; season with salt. Place in oven to keep warm. Repeat with remaining breaded schnitzel, adjusting heat to maintain oil temperature and adding more as needed.
Divide schnitzel among plates. Top with gravy and parsley.