Preheat the oven to 200 degrees F (95 degrees C). Line a rimmed baking sheet with paper towels, and set a wire rack inside.

Bring a large pot of lightly salted water to a rolling boil. Cook fettuccine at a boil until tender yet firm to the bite, about 8 minutes. Drain pasta in a colander over a heatproof bowl; reserve 1 ½ cups pasta cooking water. Set fettuccine aside, and reserve pot.

While pasta cooks, stir together breadcrumbs, flour, and ½ cup Asiago in a shallow dish until combined. Pour milk into a separate shallow dish. Season chicken on both sides with 1 teaspoon of the salt and ¼ teaspoon of the pepper. Working with 1 cutlet at a time, dredge chicken in breadcrumb mixture. Dip in milk, and coat again in breadcrumb mixture, pressing firmly to adhere. Place prepared chicken on a plate.

Pour oil to a depth of ¼-inch in a large skillet; heat oil over medium-high heat to 350 degrees F (175 degrees C). Place prepared chicken in hot oil, and pan-fry until golden brown and cooked through, 2 to 3 minutes per side. Transfer fried chicken to the prepared wire rack. Once all chicken is fried, remove paper towels.

Place the baking sheet in the preheated oven to keep chicken warm until ready to serve.

Melt butter over medium heat in the reserved pasta pot. Add garlic, and cook, stirring constantly, until fragrant and butter is foamy, about 2 minutes. Stir in heavy cream, and cook until bubbling, about 2 minutes. Whisk in remaining 2 cups Asiago, stirring constantly until thickened, 1 to 2 minutes.

Add cooked pasta, and remaining 2 teaspoons salt and ¼ teaspoon pepper; cook, stirring constantly, until pasta is coated in sauce, about 2 minutes, adding reserved cooking liquid as needed, ¼ cup at a time, to thin the sauce.

Slice chicken. Divide pasta among 4 large plates; top evenly with chicken, and garnish with parsley.