Preheat your oven to 250°F (120°C). Place a wire rack over a baking sheet and set it aside.
Cut each chicken breast in half horizontally to make thin cutlets. If they are uneven, place them between two pieces of plastic wrap and pound them to a 1/2-inch (1.25 cm) thickness. Season both sides of the chicken with the sea salt.
Crack the eggs into a wide, shallow bowl and beat them well. In a second shallow bowl, whisk together the flour, cornstarch, garlic powder, black pepper, and cayenne pepper.
Dip one chicken cutlet into the beaten eggs, letting any excess drip off. Transfer it to the flour mixture and press down firmly so the coating sticks to both sides. Place the coated chicken on a clean wire rack and let it rest for 10 minutes. Repeat with the remaining chicken.
Pour about 1/2 inch (1.25 cm) of neutral oil into a large heavy skillet. Heat the oil over medium-high heat until it reaches 350°F (175°C) on a deep-fry thermometer.
Carefully lower a few chicken cutlets into the hot oil. Do not overcrowd the pan. Fry for 3 to 4 minutes per side until golden brown and the internal temperature reaches 155°F (68°C).
Transfer the fried chicken to the prepared wire rack on the baking sheet and place it in the warm oven. The chicken will continue cooking in the oven until it reaches a safe internal temperature of 165°F (74°C).
Let the oil come back to 350°F (175°C) before frying the next batch. Repeat until all the chicken is cooked.