Step 1Heat the oil in a tall 8-quart stockpot over medium-high heat. Add the leeks, carrots and celery and cook until tender, about 5 minutes, stirring occasionally.
Step 2Add the garlic, peppercorns, bay leaf, parsley, fennel and thyme. Add 10 cups cold water. Bring to a boil over high heat, then reduce the heat, cover and cook at a hard simmer 35 minutes.
Step 3Remove the pot from the heat. Strain the stock through a fine mesh strainer, gently pressing the vegetables to extract liquid. Discard the vegetables. You should have 9 cups of stock.
Step 1Trim the feathery fronds and stems from the fennel bulbs. Chop 1 tablespoon of the fronds and reserve. Cut the bulbs in half lengthwise and remove the cores. Thinly slice on a mandoline.
Step 2Peel the onions, then very thinly slice on a mandoline.
Step 3Heat the oil in a heavy 5 1/2 -quart sauce pot and saute the fennel, onions and sugar over high heat for 5 minutes. Reduce the heat to medium and cook until the vegetables are very tender and lightly browned, 30 to 40 minutes.
Step 4Add the wine and simmer 1 to 2 minutes or until the wine is almost evaporated. Add the vegetable stock and salt. Cover and simmer 20 minutes to blend flavors.
Step 5Add the Armagnac, if using, and simmer, uncovered, 10 minutes. Stir in the reserved chopped fennel fronds. Season to taste with salt.
Step 6Put the baguette slices on a baking sheet. Broil until golden brown and crisp, about 45 seconds to 1 minute. Rub each slice with the cut garlic clove, then turn and brown the other side, about 20 seconds. Serve the soup with the garlic toasts on the side.