Almost exactly a year ago, I wrote about our daily family bowl of miso soup (well, not actually daily anymore, but 3-4 times a week), and one thing I never really thought about is that miso soup made the traditional way cannot be vegetarian because the base is really the dashi, or fish stock. Using just water will make a much weaker soup, and using vegetable stock will change the flavor quite a bit. Luckily, my copy of the Book of Miso Soup* comes to the rescue with a seaweed-only dashi recipe that you can substitute for regular fish-based dashi!
for each cup of stock you want, you will need 1 cup of water and one 2" x 4" strip of kombu.
wipe kombu down with damp paper towel. Using scissors, cut several slits partway through each strip (do not cut through). Place in a saucepan with the water and let stand 30 minutes. Put on low heat and bring to a simmer. When the water begins to bubble, remove kombu with tongs or strainer.
At this point, you can continue adding ingredients to make your miso soup, or you can refrigerate the dashi to use later. I also see no reason that you couldn't make a big batch, and freeze it in 1-2 cup servings. I doubt it would last incredibly long in the freezer, but certainly it ought to be fine for up to a month.
*I highly recommend this book to anyone who likes miso soup. The information in it is unbelievable, from a breakdown of every variant of miso to a guide on making your own, with over 100 recipes for different miso soups, each accompanied by color photos of not just the final product, but the ingredients as they should look prepped for cooking! One of the best designed cookbooks I own.