Carefully slice each chicken breast in half lengthwise to create two thin pieces (as if you were butterflying them, but continue slicing all the way through). Pat chicken dry on all sides with a paper towel - this will help the breading adhere. Season chicken with salt and pepper and set aside.
In a shallow bowl, whisk egg. In a second shallow bowl, combine bread crumbs, cajun seasoning, and garlic powder.
Place one piece of chicken into the egg mixture, flip to coat, then pick up and gently shake to remove any excess. Next, place chicken into breading mixture, flipping to coat. Use your hands to gently pat breading into the egg mixture. Gently shake to remove any excess and place breaded chicken onto a plate. Repeat with each chicken breast.
*At this point, I recommend starting your grits. When your grits are about halfway through cooking, begin frying your chicken. Or, cook your grits to completion, remove from heat, and cover to keep warm while your chicken cooks.
In a pan over medium heat, add oil. When hot, add breaded chicken, making sure not to overcrowd the pan (you may need to cook in 2 batches). Cook for about 3-4 minutes per side, OR until breading is golden brown and chicken lifts easily from the pan. Transfer to a plate and allow to rest for 2 to 3 minutes before slicing into thin strips.
In a saucepan over medium heat, add milk, chicken broth, and salt. Bring to a boil, then slowly whisk in the grits.
Reduce heat to medium-low and cook for 20 minutes, whisking frequently. If grits begin to stick to pan, reduce heat and add a splash of water. Grits should be creamy and thick, with no rough texture remaining when they're done cooking.
Remove from heat and add pepper, butter, and shredded cheese. Stir until melted. Portion into bowls and top with sliced chicken and hot sauce, to taste. Serve immediately.
To prevent breading from falling off your chicken: make sure to pat your chicken breasts dry before beginning. Shake off any excess egg and bread crumbs. When cooking, resist the urge to nudge your chicken around or move it prematurely. When your chicken is ready to be flipped, it will release easily from the pan.
To ensure your chicken is cooked through, I suggest using a meat thermometer. Chicken is cooked through when an internal temperature of 165 degrees Fahrenheit is reached at the thickest part of the meat.