Bring a large pot of salted water to a boil. Add penne and cook according to package directions until al dente. Reserve 1 cup of pasta water before draining.

While pasta cooks, season chicken cubes with salt and pepper. Heat olive oil and 1 tbsp of butter in a large skillet over medium-high heat. Add chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from the skillet and set aside.

In the same skillet, melt the remaining 2 tbsp of butter over medium heat. Add minced garlic and red pepper flakes, and cook for 30 seconds until fragrant. Add broccoli florets and a splash of chicken broth. Cover and steam for 3-4 minutes until tender-crisp.

Pour in the remaining chicken broth and heavy cream. Bring to a simmer, scraping up any browned bits from the bottom. Cook for 2-3 minutes to thicken. Stir in the Parmesan cheese and Italian seasoning until the cheese is fully melted and the sauce is smooth.

Return the cooked chicken to the skillet. Add the drained penne. Toss everything together to coat in the sauce. If the sauce is too thick, add a splash of reserved pasta water. Season with more salt and pepper to taste. Serve immediately.