Pound the chicken pieces to an even 1/2-inch thickness. Place chicken in a bowl and cover with buttermilk, salt, and pepper. Marinate for at least 30 minutes or up to 4 hours in the refrigerator.
In a shallow dish, whisk together the flour, cornstarch, paprika, and garlic powder.
Remove chicken from buttermilk, letting excess drip off. Dredge the chicken thoroughly in the flour mixture, pressing firmly to coat well.
Heat about 2 inches of vegetable oil in a deep skillet to 350°F (175°C).
Carefully place chicken pieces into the hot oil, ensuring not to overcrowd the pan. Fry for 4 to 6 minutes per side until golden brown and cooked through (internal temperature of 165°F or 74°C). Remove chicken and place on a wire rack to drain.
While the chicken rests, prepare the sauce. Melt the butter in a small saucepan over medium heat. Add minced garlic and cook until fragrant, about 1 minute.
Stir in the heavy cream and bring to a gentle simmer. Reduce heat to low. Whisk in the grated Parmesan cheese until the sauce is smooth. Stir in parsley, salt, and pepper. Keep warm.
Lightly toast the sandwich buns. Place a slice of cheese on each hot chicken cutlet, if using, and let it melt slightly.
Brush or spoon the garlic parmesan sauce generously over the top of each chicken cutlet.
Assemble the sandwich: place the sauced chicken on the bottom bun and top with the other half of the bun. Serve immediately.
Notes
For extra crispiness, double dredge the chicken: dip coated chicken back into the buttermilk, then back into the flour mixture.
If you prefer an air fryer method, spray the coated chicken with cooking spray and air fry at 380°F (195°C) for 12-15 minutes, flipping halfway.
Add a pinch of red pepper flakes to the sauce for a slight spicy kick.