1. Place chicken, carrots, onions, celery, bay leaf, parsley, wine, and peppercorns in a stockpot. Add water to cover (about 3 quarts); bring to a boil. Reduce heat so liquid is at a bare simmer. Poach, adjusting heat to maintain bare simmer and skimming any scum off the top, until chicken is cooked, 20 to 25 minutes.

2. Remove chicken from stock; use a sharp knife to remove meat from bones. Place meat in a dish; add stock to just cover. Return bones to pot; simmer until very flavorful, about 1 hour. Pass stock through a cheesecloth-lined strainer; discard solids.

3. In a clean saucepan, return stock to a boil. Reduce heat so stock is at a bare simmer. Add apricots and pineapple and poach until tender, about 10 minutes. With a slotted spoon, remove fruit; season fruit with 1/4 teaspoon salt, 1/8 teaspoon pepper, and 1/4 teaspoon tarragon.

4. Raise heat to high; cook stock until reduced to 1/3 cup, 45 minutes. Reduce heat to low; whisk in mustard, 1/4 teaspoon each salt and tarragon, and 1/8 teaspoon pepper.

5. Divide the lettuce among 4 plates. Slice chicken; place on greens. Pour mustard sauce over chicken and serve with reserved apricot-and-pineapple mixture.