Preheat the oven to 425°F (220°C). Line a baking sheet with foil and grease it lightly. Bring a medium pot of lightly salted water to a boil for the pasta.
Set out two shallow dishes. Pour the milk into one dish. Place the panko in the other dish and stir in the 1/4 teaspoon salt and 1/4 teaspoon pepper.
Butterfly the 8-ounce chicken breast by slicing it horizontally to create two even, thin cutlets.
Coat each chicken cutlet first in the milk, letting excess drip off, then press into the seasoned panko to fully coat. Place the breaded cutlets on the prepared baking sheet.
Bake the breaded chicken for 10 minutes, or until an instant-read thermometer inserted into the thickest part registers 150°F (65°C).
While the chicken bakes, heat the red sauce in a small saucepan and cook the fettuccine according to package instructions; drain when done.
When the chicken reaches 150°F, spoon about 2 tablespoons of sauce over each cutlet. Sprinkle the mozzarella and Parmesan evenly over the chicken.
Return the chicken to the oven and bake until the cheese is melted and the chicken reaches 160°F (71°C), about 5 more minutes.
Remove the chicken from the oven and let rest for 5 minutes. Plate the fettuccine, spoon remaining sauce over the noodles, and place the chicken on top to serve.