Cook the fettuccine in a large pot of salted boiling water according to package instructions until al dente. Reserve 1/2 cup of the pasta water, then drain.

While the pasta cooks, heat olive oil in a large skillet over medium heat. Add the chicken strips, season with salt and pepper, and cook until golden and cooked through, about 5 to 7 minutes. Remove chicken from the pan and set aside.

In the same skillet, melt the butter. Add minced garlic and cook for about 30 seconds until fragrant, being careful not to burn it.

Pour in the heavy cream and chicken broth. Bring to a gentle simmer, stirring to combine. Let it simmer for 2 to 3 minutes to slightly thicken.

Add the Parmesan cheese and stir until the sauce is smooth and creamy. Return the chicken to the pan and add the broccoli florets. Simmer until the broccoli is tender but still bright green, about 3 to 4 minutes.

Toss the cooked pasta into the sauce, adding a splash of the reserved pasta water if needed to loosen the sauce. Stir until everything is well coated and heated through. Adjust seasoning with salt and pepper if desired.

Serve immediately, garnished with chopped parsley if you like. Enjoy a comforting plate of creamy goodness with a touch of green for balance.