Heat olive oil in a stock pot over medium heat and sear onion, cut side down, and garlic until well-colored, about 5 minutes. Stir in mushroom stems, carrots and leeks, and cook for another 3 minutes.
Pour in water, and scrape up any browned bits stuck to the bottom of the pan. Add bay leaves, thyme sprigs and miso, and bring to a boil. Redice heat to medium-low, add dried porcini and cheese rinds, and simmer for 40 minutes. Strain well.
Cool, refrigerate, and use within a week. To freeze, let cool, and then ladle into muffin tins, and freeze. When frozen, pop stock out of the muffin tins, and store in a Ziploc freezer bag.