Boil the pasta in well-salted water until al dente, adding the broccoli during the final minute; reserve some pasta water, then drain both. The broccoli should turn bright green and remain tender with a little bite.
Warm a large pan over medium heat, add the olive oil, season the chicken with the garlic powder, paprika, italian seasoning, salt, and pepper, then place it in the pan. The chicken should sizzle steadily rather than smoke.
Cook the chicken for 5-6 minutes on each side until cooked through, then transfer it to a plate and let it cool for 5 minutes before slicing or dicing. The center should no longer look pink, and the outside should have golden seasoning marks.
Add 1 tablespoon olive oil and the onion to the unwashed pan, cooking for 3-5 minutes before stirring in the garlic for about 30 seconds. The onion should soften, and the garlic should smell fragrant and just begin to turn golden.
Whisk in the flour and cook it for about 30 seconds, then gradually whisk in the chicken stock and whole milk until smooth. The flour should smell lightly toasted, not doughy, before the liquids go in.
Bring the sauce to a gentle simmer, then whisk in the cream cheese and Parmesan until smooth; season with salt and pepper as desired. The sauce is ready when it coats the back of a wooden spoon in a thin, even layer.
Fold the drained pasta and broccoli into the sauce, then toss with the sliced or diced chicken or arrange the chicken over each serving. The noodles should look evenly coated; add reserved pasta water if the sauce tightens too much.
Finish with more Parmesan cheese or parsley, if desired. Serve while the sauce is glossy and creamy.