Roast the garlic and potatoes (oil-free roasted garlic method source):
Preheat the oven to 400 degrees Fahrenheit. Slice off the top of the head of garlic, partly exposing all of the individual cloves. Completely wrap the head of garlic in foil and place on a baking sheet or in a muffin tin. Do the same with the diced potatoes, making 2 or 3 wrapped foil pockets with about 1/2 cup each of potato in them.
The garlic will be done in about 45 minutes, or when completely soft. Unwrap the foil and let it cool, then squeeze the roasted garlic out of the cloves, and mash them with a fork if needed to break them up. The potato will be done in 30-35 minutes.
Caramelize the shallots:
Melt the coconut oil in a large saucepan. Add the sliced shallots, vinegar, and a sprinkle of salt, and stir to coat. Let cook over medium-low heat, stirring occasionally, for about 40 minutes, or until shallots are thoroughly browned.
Make the soup:
When the shallots are done, add the minced fresh garlic and celery to the saucepan, and cook for a minute or two to soften. Whisk the miso into a bit of water and add it along with the wine, white beans, and vinegar, along with about a cup of water, more or less depending on how thick of a stew you like.
Bring the mixture to a boil, then reduce the heat to medium. Add the roasted garlic and cooked potatoes and stir.
Cook for another 10-15 minutes, or until celery is fully cooked, wine is cooked off and flavors are incorporated. Add oregano, chili flakes, fresh thyme, salt and pepper to taste.
Notes:
This soup freezes great (that's how I bring soup to work for lunch, since in its frozen form it does not leak all over my backpack).
Regular balsamic vinegar can always be used instead of white, but will affect the color.