Bring a large pot of salted water to a boil, then add pasta and cook according to package directions. While pasta cooks, heat 3 tbsp olive oil in a large skillet over medium-high heat until shimmering.
Season chicken pieces with salt and pepper, then cook in the hot skillet for 6-7 minutes per side until golden and cooked through. Transfer cooked chicken to a plate and set aside briefly.
In the same skillet, add diced onion and cook for 2-3 minutes until softened and fragrant. Add minced garlic and cook an additional minute, stirring constantly to prevent burning.
Stir in tomato paste and cook for 1 minute to deepen the flavor, then add chicken broth, diced tomatoes with their juice, and Italian seasoning. Bring the mixture to a gentle simmer.
Return the cooked chicken to the skillet and reduce heat to medium-low, simmering for 5 minutes to allow flavors to meld. This weeknight chicken pasta recipe sauce should smell incredibly aromatic by now.
Stir in heavy cream and half of the Parmesan cheese, mixing until smooth and creamy. Taste and adjust seasoning as needed with additional salt and pepper.
Drain the cooked pasta and add it directly to the sauce, tossing gently to coat every piece evenly. Cook together for 2 minutes to allow pasta to absorb the delicious flavors.
Serve immediately in bowls, garnishing with fresh parsley and remaining Parmesan cheese for presentation and extra flavor.