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Bring a large pot of salted water to a rolling boil. Add 8 ounces protein pasta and 2 cups broccoli florets and cook 8–10 minutes until pasta is al dente and broccoli is tender-crisp. Scoop out and reserve 1/2 cup pasta water, then drain pasta and broccoli.
Meanwhile, heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add 1 pound boneless, skinless chicken breast pieces and sprinkle with 1 teaspoon garlic powder, 1/2 teaspoon onion powder, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Cook 5–7 minutes, stirring occasionally, until chicken is golden and reaches 165°F.
Pour 1 cup chicken broth and 1/2 cup milk into the skillet with the chicken. Bring to a gentle simmer, scraping up browned bits. Let simmer 2–3 minutes until sauce begins to thicken.
Add the drained pasta and broccoli back into the skillet. Stir in 1/4 cup grated Parmesan cheese. If the sauce is too thick, add reserved pasta water a splash at a time until creamy. Stir until everything is evenly coated.
Divide the pasta among plates and sprinkle with extra Parmesan cheese if desired. Serve immediately. Store leftovers in an airtight container in the refrigerator for up to 3 days.