Preheat oven to 425°F, prepare a cooling rack with parchment under it (this is for the chicken to rest on and let the oil drip down.) Set aside.
Prepare the greek yogurt egg replacer mixture: on a medium shallow plate or bowl, combine 3 tablespoons of plain greek yogurt, 1 tablespoon of oil, and 1/2 tablespoon water. Stir to mix well until a smooth consistency is formed.
Gather 2 other medium sized plates or shallow containers. One plate is for flour plus a dash of salt and pepper. Another plate is for for the greek yogurt mixture. The third plate is bread crumbs/panko.
Pat thinly sliced chicken breasts dry with paper towels. Dredge each sliced chicken breast in flour, patting off excess, then dredge each piece of chicken in the yogurt-mixture, sliding excess mixture off with your fingers so it is a light coating. Finally dredge all pieces in panko bread crumbs. Be sure to press the chicken well into the crumbs, getting into all nooks and crannies.
Heat a dutch oven or tall walled cast iron with about 1-2 inches of oil, target temperature of oil between 325-350°F. If you don’t have a food thermometer, dip a wooden chopstick in and watch for bubbles to sizzle around it. If no bubbles arise, the oil is likely too cool and not ready. One at a time, slowly lower dredged chicken into hot oil. When the pan-side chicken looks golden, carefully turn chicken over, usually 1-2 minutes per side. Internal temperature of chicken should be at least 165°F. Set on wire rack to let grease drip off. Immediately salt the hot chicken straight out of the fryer. Repeat process with remaining chicken pieces.
Place fried chicken on sheet pan, add desired amount of sauce and cheese. Bake until cheese is golden or melted. Approximately 10 minutes.
Serve alongside your favorite pasta dish, a salad, or garlic bread!