Place both mushrooms, carrot, celery root, shallots, and rosemary leaves in the bowl of a food processor; process until finely chopped.
Heat vegetable oil in a large pot over high heat. Transfer vegetable mixture to pot and reduce heat to medium. Cook vegetables, letting them "cake" in bottom of pot, about 5 minutes.
Add 12 cups water to pot. Simmer for 2 hours. Strain stock and let cool.