I haven't mastered parsnips yet by any means. I've only made them a couple times and I wasn't a big fan of the results, so someday I'll attack them from a different angle. They are a little bit like a cross between a carrot and a turnip in flavor, I find, which makes them challenging to use unless you really like their taste. The best resource I've ever found for what to do with all sorts of winter veggies is a cookbook called Recipes from the Root Cellar. She does some truly magical things with root veggies (also squash, kale, etc.) and I use it ALL winter. Her basic overview of parsnips says they are best roasted-- again that makes them a strong roasted carrot-turnip flavor-- and to be careful putting them into soups so that you don't add too much sweetness. Other than that I'm really not sure.
You can do basically anything you want with squash and it usually turns out nicely. Since you haven't purchased any yet, I would recommend picking up some butternut squash. They're easy to work with and have a good smooth texture. An easy thing to do with them is cut them in half lengthwise (don't peel), scoop out the seeds (reserve them for roasting if you want), stuff them with tasty things and bake them. There are a lot of recipes out there for that. They're also great for making into velvety pureed soups. Good things to throw in there are apples, sage, a splash of half-and-half, curry powder, and coconut milk (not all together, obviously). Good toppings are the roasted seeds and fried sage leaves. You can also make a mash of them and you would want to whip them really well with a wooden spoon. They go nicely in all sorts of baked goods when pureed (think quick bread, waffles, pancakes, etc.). I've never been a big fan of serving them in cubes since they are at their best when they are really soft but you can roast them and put them in stews and things like that as well.