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

Lightly flour the chicken: Place the flour in a shallow bowl or plate. Coat each cutlet lightly on both sides and shake off the excess.

Boil the pasta water: Bring a 5- to 6-quart pot of water to a rolling boil and add 1 tablespoon fine salt.

Cook the pasta: Add the pasta and cook according to the package directions until al dente, usually 9 to 12 minutes depending on the shape.

Reserve pasta water: Before draining, scoop out 1 cup (240 ml) of the starchy pasta cooking water. Drain the pasta without rinsing.

Sear the chicken: While the pasta cooks, heat the olive oil and 1 tablespoon (14 g) butter in a 12-inch deep skillet over medium-high heat. Add the chicken in a single layer, working in batches if necessary. Cook for 3 to 4 minutes on the first side until golden.

Finish the chicken: Turn and cook for another 2 to 4 minutes, until the thickest part reaches 165°F (74°C). Transfer to a clean plate and let rest for 5 minutes.

Brown the mushrooms: Reduce the skillet heat to medium and add the remaining 2 tablespoons (28 g) butter. Add the mushrooms in an even layer and cook for 5 to 7 minutes, stirring only occasionally, until their moisture evaporates and the edges become golden brown.

Add the garlic and thyme: Stir in the garlic and dried thyme. Cook for about 30 seconds, until fragrant but not browned.

Deglaze with Marsala: Pour in the Marsala wine and scrape the bottom of the skillet to loosen the browned bits. Simmer for 3 to 4 minutes, until the wine has reduced by roughly half and the sharp alcohol aroma has softened.

Add the broth: Pour in the chicken broth and simmer for another 3 minutes. The liquid should reduce slightly but still cover the bottom of the skillet.

Add the cream: Reduce the heat to medium-low and stir in the heavy cream and remaining 1/4 teaspoon salt. Bring to a gentle simmer for 2 to 3 minutes.

Add the Parmesan: Reduce the heat to low: Add the Parmesan gradually, whisking until smooth after each addition. Do not allow the sauce to boil.

Adjust the sauce: Stir in 1/2 cup (120 ml) of the reserved pasta water. The sauce should be creamy, glossy, and loose enough to flow slowly from a spoon.

Add the pasta: Transfer the drained pasta to the skillet and toss for 1 to 2 minutes until evenly coated. Add additional reserved pasta water a few tablespoons at a time if the sauce becomes too thick.

Finish with lemon: Remove the skillet from the heat and stir in the lemon juice. Taste and adjust seasoning only if needed.

Slice the chicken: Slice the rested chicken across the grain into strips.

Assemble and serve: Arrange the sliced chicken over the creamy Marsala pasta or gently fold it into the skillet. Garnish with parsley, extra Parmesan, or black pepper if desired.