Cook pasta until al dente — 10 minutes or less — or according to instructions on the box.
Add olive oil into a large pot over medium-high heat. Add in chicken, rosemary and garlic and cook until cooked through, about 10 minutes, depending on the size of your chicken chunks. Avoid fussing with the chicken, but feel free to give it the occassional turn to ensure both sides cook evenly. Remove chicken and set aside, leaving fat in the pan (it’s OK to leave some herbs and chicken bits, too).
Add zucchini and cook for about 10 minutes. Salt zucchini well to help excess water to cook off. Again, avoid fussing with the zucchini.
Add stock and milk into the pan, then stir in parmesan. Continue to stir until cheese melts into the suace. When sauce starts to thicken (after about 7-13 minutes), stir in pasta and chicken until evenly coated in sauce. If sauce is still not at your desired consistency, give it another few minutes on the stove. Serve while hot and garnish with additional parmesan, if desired!