Add onions, milk, chicken broth, broccoli, pepper, and salt to the slow cooker and mix until well combined.
Cover and cook on low for 4 hours.
Add cheese cubes to slow cooker; stir until melted.
Add cheddar and Parmesan and stir until melted. Immediately turn off slow cooker to avoid curdling.
Serve warm.
Notes
Refrigerate the leftovers in an airtight container for up to 5 days. If you plan to freeze it, I suggest doing it right away, so it freezes at its best.