Steam the broccoli. Pour ¼ inch of water into a wide, deep pan with a lid and bring to a boil. Add 3 cups broccoli florets, cover, and cook over medium heat for 4–5 minutes, until a thick stem is fork-tender (1–2 minutes more if needed). Transfer to cold or ice water, drain thoroughly, and set aside. Discard the water in the pan.
Make the aromatic water. In the same pan, combine 8 cups water, 5 smashed garlic cloves, ½ medium onion thinly sliced, 4–5 thin lemon slices, and 2 teaspoons fine table salt. Bring to a boil, then reduce the heat and gently simmer for 5 minutes.
Poach the chicken. Add 1–1¼ pounds chicken breast cut into 1-inch cubes. Keep at a gentle simmer. Start checking at 6 minutes; the pieces may take 8–10 minutes after the water returns to a simmer. Check that the largest pieces reach 165°F/74°C.
Remove the chicken and aromatics. Scoop the cooked chicken onto a clean plate. Remove and discard the lemon, garlic, and onion. Keep the cooking liquid in the pan.
Cook the macaroni. Bring that liquid back to a boil. Add 3 cups dry macaroni and cook according to the package directions, stirring occasionally.
Reserve water and drain. Save 1 cup cooking liquid, then drain the macaroni.
Alfredo sauce. In the same pan, melt 4 tablespoons butter over medium-low heat. Stir in 1 ½ cups heavy whipping cream, ½ teaspoon onion powder, and ¼ teaspoon black pepper. Gently simmer for 2–3 minutes. Turn off the heat and let the bubbling settle. Gradually stir in 1 cup freshly, finely grated Parmesan (about 90 g) until smooth.
Combine. Add the macaroni, cooked chicken, and any chicken plate juices. Toss, then gently fold in the steamed, well-drained broccoli.
Adjust and serve. Add reserved cooking liquid 2 tablespoons at a time if the sauce needs loosening. Warm gently over low heat without boiling. Taste before adding more salt, and serve immediately.