Pat the chicken cutlets dry with paper towels: Season both sides with 3/4 teaspoon of the salt, the black pepper, and Italian seasoning.

Bring a 5- to 6-quart pot of water to a rolling boil. Add 1 tablespoon fine salt, then add the linguine.

Cook according to the package directions until al dente, generally 9 to 11 minutes. Before draining, reserve 1/2 cup (120 ml) of the starchy cooking water. Drain the pasta without rinsing.

While the pasta cooks, heat the olive oil and 1 tablespoon (14 g) of the butter in a 12-inch skillet over medium-high heat.

Add half of the chicken cutlets in a single layer. Cook for 3 to 4 minutes, until the underside is golden brown and releases easily from the skillet.

Turn the cutlets and cook for another 2 to 4 minutes. Transfer them to a clean plate when the thickest portion reaches 165°F (74°C). Repeat with the remaining chicken, adding the remaining 1 tablespoon (14 g) butter as needed.

Let the cooked chicken rest for 5 minutes while preparing the garlic butter sauce.

Reduce the skillet heat to medium-low: Add 2 tablespoons (28 g) of the 4 tablespoons butter for the pasta. Add the minced garlic and cook for 30 to 45 seconds, stirring continuously. The garlic should smell fragrant but remain pale.

Pour in the chicken broth and scrape the bottom of the skillet to release the browned chicken bits. Add the remaining 1/4 teaspoon salt and simmer for 2 to 3 minutes, until the broth reduces slightly.

Add the drained linguine and the reserved 1/2 cup (120 ml) pasta water to the skillet. Toss over medium-low heat for about 1 minute.

Add the remaining 2 tablespoons (28 g) butter a little at a time while tossing the pasta. The liquid should become glossy and lightly coat the noodles rather than appearing oily.

Reduce the heat to low: Sprinkle in the 3/4 cup (68 g) Parmesan in two or three additions, tossing continuously until melted. If the pasta looks dry, add 1 to 2 tablespoons of warm water.

Remove the skillet from the heat: Add the lemon juice and chopped parsley, then toss until evenly distributed. Taste before adding any additional salt.

Cut the rested chicken across the grain into strips. The interior should be opaque and juicy with no translucent areas.

Divide the garlic butter linguine among six plates or shallow bowls. Arrange the sliced chicken over the pasta.

Top with additional Parmesan, crushed red pepper flakes, and lemon wedges as desired. Serve immediately while the sauce is glossy and warm.