In a large pot or deep skillet, combine whole milk and water (or vegetable broth). Bring to a rolling boil over medium-high heat.
Add pasta to the boiling liquid and immediately reduce heat to a gentle simmer. Cook for 10 minutes, stirring occasionally to prevent sticking. The liquid will become thicker and creamier as pasta releases its starches.
Stir in finely chopped broccoli and continue to cook for 2-3 minutes until both pasta and broccoli are cooked to your liking. Broccoli should be tender but still bright green.
Remove pot from heat completely. Stir in shredded cheddar cheese, Greek yogurt, and butter (if using) until cheese melts completely and sauce becomes smooth and glossy. The residual heat will melt everything perfectly without making the sauce grainy.
Serve immediately while hot and creamy. The sauce will thicken as it sits, which is normal.