Place the 4 chicken cutlets in a large resealable bag and add 2 cups buttermilk, 2 teaspoons salt, and 2 teaspoons pepper; seal and shake to coat. Marinate at room temperature for 1 hour.
Pour enough vegetable oil into a large skillet to come about halfway up a cutlet and heat over medium-high until shimmering and hot.
In a large bowl, whisk together 2 cups flour, 2 teaspoons paprika, 2 teaspoons garlic powder, 1 teaspoon salt, 1 teaspoon pepper, and 1 teaspoon cayenne.
In a separate small bowl, beat the 2 eggs until combined.
Remove one cutlet from the marinade and let excess drip off. Dredge it thoroughly in the seasoned flour, then dip into the beaten eggs, and return to the flour for a final, even coating.
Carefully place the breaded cutlet into the hot oil (oil should cover about half the cutlet). Fry 5–7 minutes per side, until golden brown and cooked through. Transfer to a paper towel–lined plate and repeat with remaining cutlets.
After frying all cutlets, wipe out excess oil from the skillet or use a saucepan; melt 1/2 cup butter over medium heat. Whisk in 1/2 cup flour to form a roux and cook 1–2 minutes until bubbly.
Slowly whisk in 2 cups chicken broth until smooth. Season with salt and pepper to taste and simmer until the gravy reaches your desired thickness.
Serve the fried chicken smothered with the gravy.