Preheat the oven to 425°F. Line a baking sheet with foil and grease the foil. Put a medium pot of lightly salted water on the stove and bring it to a boil for the pasta.
Pour 1/3 cup milk into a shallow dish. Put 1/3 cup panko into a second shallow dish and stir the 1/4 teaspoon salt and 1/4 teaspoon pepper into the panko.
Place the 8-ounce boneless skinless chicken breast on a cutting board. Using a sharp knife, butterfly it by slicing horizontally through the center to make two even, thinner pieces (cut all the way through so you have two separate cutlets).
Dip each chicken piece into the milk, letting excess drip off, then press each piece into the seasoned panko to coat both sides. Transfer the coated cutlets to the prepared baking sheet.
Bake the chicken on the middle oven rack for 10 minutes.
While the chicken bakes, heat 1 1/2 cups of your favorite red sauce in a small saucepan over low heat and cook the 4 ounces fettuccine according to package instructions. Keep the sauce warm; reserve some of it for the pasta.
After the initial 10 minutes of baking, remove the chicken from the oven. Spoon a small amount of the warm red sauce over each chicken piece (reserve the remaining sauce for the pasta). Evenly sprinkle the 1/2 cup shredded mozzarella and 1/4 cup shredded Parmesan over the two cutlets.
Return the chicken to the oven and bake until the cheese is melted and the chicken is cooked through. Use a meat thermometer to confirm an internal temperature of 165°F, about 4–6 more minutes depending on your oven.
Remove the chicken from the oven and let it rest for 5 minutes. Drain the fettuccine and toss it with the reserved sauce. Divide the noodles between two plates and serve each chicken cutlet on top of the pasta.