Heat oil in a large Dutch oven over medium-high heat. Add onion and carrot; sauté 8 minutes or until onion begins to brown.
Remove roots, outer leaves, and top 6 inches from leeks. Rinse well and drain. Reserve remaining portion for another use. Chop leek outer leaves and tops. Add roots, chopped leek, mushrooms, and remaining ingredients to onion mixture; bring to a boil. Reduce heat; simmer until reduced to 6 cups (about 30 minutes). Strain stock through a sieve over a bowl; discard solids.