Could you replace the milk with a non-dairy milk?

Tracie, FYI, most recipes I've seen for Parker House (or other dinner rolls) without dairy milk use almond milk.
Here's one, FYI, with proportions to compare to the recipe you were looking at.
https://rud.is/b/2016/02/12/dairy-free-parker-house-rolls/

Hi Tracie, I believe that you could substitute soy milk, almond milk, rice milk, or oatmilk and this Classic Parker House Rolls recipe would still turn out fine and be enjoyable. Any differences in taste or texture should be barely noticeable. Just make sure to use unsweetened non-dairy milk.