Bring a large pot of well-salted water to a boil and cook the pasta until just shy of al dente (about 1 minute less than package directions). Before draining, reserve 1 cup of the pasta water.

Place the chicken breast between two sheets of plastic wrap and gently pound it to an even thickness of about 1/2 inch (1-1.5 cm). Season both sides generously with salt and pepper, then dust with the flour, shaking off any excess.

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

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

Stir in the chopped rosemary and cook for another 30 seconds.

Pour in the heavy cream, reduce the heat to low, and bring to a gentle simmer—do not let it boil. Add the grated Parmesan in 2-3 batches, stirring well after each addition until melted and smooth.

Season the sauce with the black pepper and lemon juice, then stir in 1/4 cup of the reserved pasta water. Let the sauce simmer gently for 2-3 minutes, until it thickens slightly.

Add the drained pasta to the skillet and toss to coat evenly. Let it bubble gently for 1-2 minutes, adding a splash more pasta water if the sauce seems too thick.

Slice the rested chicken breast into strips. Serve the pasta topped with the chicken pieces, or toss them through. Garnish with extra rosemary leaves, fresh lemon zest, and additional Parmesan if desired.