Inspired by some of the answers and comments on a recent question on boiling potatoes whole or diced, I'm curious:
What's the best way to cook a combination of vegetables to be mashed? I'm thinking of a subset of potatoes, turnips, rutabagas, parsnips, carrots, and anything else that sounds good. Obviously if boiling, one wants to avoid waterlogged vegetables, but the cooking times of the various vegetables are different. Is there a reliable way to cook everything together (at least for some subsets)?
Edit: As mentioned in the comment below, I know that the best one can do may be starting with the longest-cooking vegetables and incrementally adding the rest. What I was wondering was things like if some or all were better baked, or if boiling is good, if some besides potatoes are better boiled whole...