Roasting the apples brings out their natural sweetness while adding a smoky flavor to this soup.
Toast the fennel seeds in a small dry skillet over medium heat, shaking, until aromatic. Transfer the toasted seeds to a spice mill, and grind to a fine powder. Reserve 1 1/2 teaspoons of the ground fennel. (Any remaining ground fennel may be saved in an airtight container.)
Heat oven to 450 degrees with rack in center. Spray a 9 by 12 3/4 by 2 1/2-inch roasting pan with cooking spray. Arrange the onions and the potatoes in pan. Core 2 apples, and add to pan. Spray onions, potatoes, and apples with cooking spray, and sprinkle with the cumin, reserved fennel, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Roast 25 minutes. Remove apples from pan, and let cool. Using a spatula, turn vegetables over, and continue to roast, 25 to 40 minutes, or until onions are tender when pierced with a knife.
Set aside 2 cooked potato quarters and 2 cooked onion quarters; cut into bitesize chunks, and reserve. Transfer remaining onions and potatoes to a food processor. Add 1/2 cup of chicken stock to pan; place over medium-high heat. Scrape up any cooked-on bits with a wooden spoon, and add the warm liquid to food processor. Add 1 1/2 cups stock to processor. Puree until smooth. Transfer puree to a stockpot. Remove peel from 2 cooked apples. Add the flesh to food processor. Add 1 1/2 cups stock, and puree until smooth. Transfer to the stockpot, stir, and warm over medium heat. (If soup is too thick, add the remaining 1/2 cup stock, and warm.) Season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Meanwhile, peel and core the remaining apple; cut into 1/2-inch chunks. Spray a skillet with cooking spray. Cook over medium high heat, 8 to 12 minutes, until chunks are golden brown.
To serve, add apple, potato, and onion chunks to soup, and warm over medium heat. Season to taste. Sprinkle with tarragon.