Submerge cutlets in pickle brine; refrigerate 45 to 60 minutes. Drain; pat lightly dry.
Whisk buttermilk and egg in a shallow bowl. Mix flour, cornstarch, garlic powder, pepper, and salt in another.
Dip cutlets in buttermilk mixture; press into flour. Squeeze a few damp coating clumps onto surface.
Rest breaded cutlets on a rack 10 minutes while oil heats.
Heat 1 inch oil in a wide Dutch oven to 350°F.
Fry two cutlets at a time, 3 to 4 minutes per side, keeping oil near 340°F, until crisp and 165°F in thickest spot.
Drain on a rack 5 minutes; paper towels soften bottom crust.