In a large pot, bring salted water to a boil. Add the fettuccine and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1/2 cup of pasta water, then drain and set aside.
In a large skillet, heat olive oil over medium heat. Add the diced chicken, season with salt, pepper, and Italian seasoning, and sauté until cooked through and golden brown, about 6-8 minutes. Set aside.
In the same skillet, add more olive oil if needed, and sauté the broccoli for about 3-4 minutes until bright green and tender-crisp. Add minced garlic and cook for an additional minute.
Reduce heat to low, pour in heavy cream, and bring to a gentle simmer. Gradually whisk in Parmesan cheese until melted and smooth. Adjust consistency with reserved pasta water if needed.
Add cooked fettuccine and sautéed chicken back into the skillet, tossing until well coated. Adjust seasoning with salt and pepper if necessary. Serve immediately, garnished with extra Parmesan if desired.