Heat oven according to directions on the package of biscuits.
Attach a deep-frying thermometer to the side of a large Dutch oven or heavy-bottomed pot. Heat about 2 1/2 inches of oil over medium to 325 degrees F Line a baking sheet with paper towels.
In a medium bowl whisk together wet ingredients, place chicken into marinade. Meanwhile, as oil heats, in a medium bowl, whisk together dry ingredients.
Reserving the marinade, remove the chicken to a plate. Whisk the egg into the marinade.
Dip the chicken into the egg mixture, one piece at a time, shaking off excess egg mixture. Dredge chicken piece in flour mix, making sure to coat evenly on both sides. Repeat the breading process (egg mixture to flour mixture) one more time, set chicken aside.
Once oil is heated, cook chicken until golden brown on each side, about 2 to 3 minutes a side. Chicken should be opaque in the center. As chicken cooks, prepare biscuits according to package directions. Place cooked chicken on prepared baking sheet to drain. Set biscuits aside.
Heat the oven to 350 degrees F Generously spray a small rimmed baking sheet (9x13) with cooking spray. In a medium bowl, reserving the sliced cheddar cheese, whisk together ingredients for folded eggs until pale in color and frothy. Pour egg mixture into the prepared baking sheet. Cook until slightly wobbly, but set in the center, about 6 to 8 minutes, rotating pan halfway through.
Cover baking sheet with cutting board for 4 minutes, or until egg is set in center, but still tender.
With two hands, use kitchen towels to sandwich baking sheet and cutting board. Flip “sandwich” over, placing board on kitchen counter. Lift pan and slice cooked egg crosswise into 5 even strips. Gently fold each slice in half lengthwise and transfer, using a thin spatula, back onto baking sheet. Top with cheese and bake for 2 to 3 minutes, or until cheese is melted.
Split each biscuit in half and top each with chicken, egg, and remaining biscuit top. Serve immediately.