Step 1Heat the oven to 425 degrees. Toss together the onion, carrots, celery, garlic and celery root with the olive oil, salt and pepper in a large baking pan. Roast 35 to 45 minutes or until vegetables are lightly browned, stirring occasionally.
Step 2Place the roasted vegetables in a tall 8-quart stockpot. Cut the leeks into quarter-inch slices and add them to the pot. Add the peppercorns, bay leaf, thyme, parsley and dried mushrooms. Peel the potatoes and add the peels to the pot. Cut the peeled potatoes into half-inch dice, cover them with cold water, and set aside to use in the soup. Add 10 cups cold water to the stockpot.
Step 3Bring the mixture to a boil over high heat. Reduce the heat to a simmer and cover. Simmer 45 minutes.
Step 4Remove the pot from the heat. Strain the stock through a cheesecloth-lined strainer, lightly pressing the vegetables with the back of a spoon to extract juices. Discard the vegetables. You will have about 8 cups of stock.
Step 1Heat the oven to 425 degrees. Toss the sliced mushrooms in a bowl with 4 teaspoons olive oil, one-eighth teaspoon salt and a pinch of white pepper. Place in a baking pan and roast for about 13 minutes, until tender and lightly browned. Remove from the oven and let stand.
Step 2Saute the onion, celery and carrot in 2 tablespoons olive oil in a tall 8-quart stockpot until tender, about 5 minutes. Add the garlic and saute 1 minute.
Step 3Add the white beans, vegetable stock, cabbage and 1 teaspoon salt. Bring the mixture to a boil over high heat, then reduce heat to a simmer, cover and cook about 1 hour, stirring occasionally.
Step 4Add the drained potatoes and the mushrooms during the last 30 minutes of cooking.
Step 5Add the green and yellow beans during the last 15 minutes of cooking and simmer until the beans are crisp-tender. Season to taste with salt. Serve the soup with toasted French bread brushed with good olive oil.