In a large saucepan or Dutch oven, heat the oil over medium-high heat. Place the shallots and garlic, cut-sides down, into the pan and caramelize for 5 minutes.
Add the mushrooms, celery, parsley stems, lemon peels, thyme, bay leaf, kombu and Parmesan rinds. Cover with the cold water and bring to a boil. Lower the heat and simmer, stirring the bottom often to prevent the rinds from sticking, until the broth is rich and aromatic, 1½ hours. Strain through a fine-mesh sieve and use immediately, or chill and store in the fridge, covered, for up to 4 days.