Put the chicken, onion, parsley stems, celery tops, and peppercorns into a saucepan with a quart of water. Bring to a simmer and cook, covered, for 45 minutes.
Remove the chicken. Debone it and put the bones into the saucepan. Return to a low boil, this time uncovered.
Chop the chicken into one-inch dice and refrigerate.
Toast the almonds in a pan in a toasted oven or a broiler at 400 degrees. When you see the first sign of browning, remove the almonds from the heat and set aside to cool.
Make the poppyseed dressing by combining all the ingredients in a bowl and whisking or blending in a food processor or blender.
In a bowl, blend the mayonnaise with the chicken base, or with 3 Tbs. of the chicken stock (if still hot, whisk in a little at a time). Add the chopped chicken meat and the sliced celery. Toss until well coated. Refrigerate.
Tear the leaves of lettuce into large pieces. Toss with the poppyseed dressing (use your judgment as to the amount) and divide into serving plates. Top with the chicken-celery mixture, then with the fruits, then with the almonds. Serve immediately.