How to prepare a vegetable base using roasted squash for savory tomato-chunk soup
Your base probably needs to be a roasted squash puree, I don't think it will work well just being used to flavor a stock. Normally you would add cream to roasted squash to make a soup, but I guess that wouldn't be vegan. Butternut squash is tasty for this (and very autumn/winter), if you haven't actually picked out your ingredients yet.

If you want to add asparagus flavor, you should consider toasting/grilling the asparagus first. Applying a dry heat to asparagus when cooking it will bring out a very savory flavor (a nice addition to a vegan dish), but just boiling it in liquid will make it taste "grassy". It all depends on what flavor you want out of it, really. Asparagus is really a spring/summer ingredient though, if you're really wanting to be "seasonal" with this dish.