How to keep homemade soup and cooking stocks/broths consumable without refrigerator?

When laboratories need to grow bacteria in a dish, they use a medium which is basically broth with gelatin--the bacteria love it. Not even normal canning will sterilize broth enough to be safe. Broth must be pressure canned, and for a long time (75 minutes at pressure for pints, 90 minutes for quarts). Many soups can be canned this way as well, but be careful not to add dairy or thickeners of any kind--the liquid must be able to distribute the heat of the pressure canner evenly throughout the jar to ensure sterilization.

I preserve vegetable, chicken, and beef stock this way with good results. Dashi has a more delicate flavor that might not hold up to it, so probably the traditional method of dehydration is best.

If you can make it acidic (sour) using lemon, vinegar, citric acid etc then it may be preserved with Sodium Benzoate. Do keep in mind the maximum permissible limits. It should not require canning or refrigeration.