Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add broccoli, cover, and steam until just tender, 2 to 4 minutes.
Combine potatoes, chicken broth, onion, and garlic in a pot over medium heat. Simmer until softened, 20 to 30 minutes. Mash about half the potatoes in the broth. Combine cream cheese and milk in a bowl; stir into the broth until incorporated. Reduce heat to low. Add Parmesan cheese gradually, stirring until melted after each addition. Add cooked broccoli.