Bring a large pot of well-salted water to a boil. Add the pasta and cook until 1 minute less than al dente. Before draining, reserve 1 cup of the pasta water. Drain the pasta and set aside.

Place the chicken breast between two sheets of plastic wrap and gently pound with a rolling pin or heavy skillet to an even thickness of about 1/2 inch.

Season both sides of the chicken generously with salt and pepper, then dust lightly with the flour, shaking off any excess.

Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook for 2 minutes per side, until golden and cooked through (internal temperature reaches 165°F). Transfer to a plate, tent loosely with foil, and set aside.

Reduce the heat to medium and add the butter to the skillet. Once melted, add the garlic and cook gently for 1 minute, stirring constantly, until fragrant but not browned.

Stir in the rosemary and cook for another 30 seconds.

Pour in the heavy cream and bring to a very gentle simmer over low heat, being careful not to let it boil.

Add the Parmesan in 2 or 3 additions, stirring until fully melted and smooth after each addition.

Season with the black pepper and stir in the lemon juice.

Add 1/4 cup of the reserved pasta water to the sauce and let it simmer gently for 2 to 3 minutes, until it thickens slightly.

Add the cooked pasta to the skillet and toss well to coat. Let it bubble gently for 1 to 2 minutes, adding more pasta water if needed for a silky consistency.

Slice the chicken breast into strips. Serve the pasta topped with the chicken, or toss the chicken pieces through the pasta.

Garnish with extra rosemary leaves, fresh lemon zest, and additional Parmesan if desired.