Preheat a large pot over medium-high heat. Saute the onion and garlic in oil with a pinch of salt for about 5 minutes, just to get a little caramelization going.Add the carrots, ginger and water. Cover and bring to a boil. Once boiling, leave the lid slightly ajar so that steam can escape, and lower heat a bit, simmering to reduce by about 1/3rd. After about 30 minutes, add the kombu. Let cook an additional 30 minutes or so, removing the kombu at this point so that it doesn’t get slimy. All said, it should simmer for a little over an hour, and reduce to 8 cups.
Add the mirin, miso and salt and stir. Let simmer for an additional 2 minutes, then turn off the heat.
Place a separate pot, large enough to manage 8 cups of broth, in the sink. Place a handled strainer so that it sits securely on top of the pot (as pictured). Line with a few layers of cheesecloth with plenty of overhang. Pour in the vegetables and broth and let strain for about 20 minutes.
Once cool enough to handle, bunch up the cheesecloth and squeeze, so that the vegetables release as much moisture and flavor as possible.
Taste for salt again, and now your broth is ready to use! Freeze in tightly sealed plastic or glass containers for up to 3 months, if not using within the week.