My mom brought us a butternut squash yesterday -- mainly to feed to Little Bear, but she wasn't going to eat the whole thing. So baked it, and then I ate some mixed with almond milk, maple syrup, and pumpkin-pie spices. And then this morning I had some sliced on toast with maple "butter" and cinnamon-sugar. I'm not usually a fan of squash, but those were yummy.

Here was the first thing that came to mind when you mentioned squashen: http://www.seletsucre.com/pumpkin-kibbe/
I haven't actually made pumpkin kibbeh before -- in fact, I may not ever have eaten it... but it is a thing some people like to do with pumpkin.

If you're pickling your beets, you might try throwing the carrots in there too. I've been pickling carrots along with cucumbers this summer and I like the result a lot. Radishes, too, if you happen to have some.