Rinse chicken, pat dry. Cut into 1" pieces. Melt butter in a skillet over medium high heat. Add mushrooms and onion; cook for 4-5 minutes, or until tender, stirring.
Add chicken, wine, tarragon, white pepper, and 1/8 tsp salt. Bring just to boiling; reduce heat. Simmer, covered, for 5 minutes, stirring once. Remove from heat.
Meanwhile, cook lasagna noodles according to package direction. Halve each noodle lengthwise. Curl each noodle into a 2.5" diameter ring and place, cut side down, in a 3-qt rectangular baking dish. Using as slotted spoon, spoon chicken mixture into center of lasagna rings, reserving the liquid in the skillet. Add the cream cheese to the reserved liquid; heat and stir just til cream cheese is melted. in a small bowl, stir together sour cream and flour; stir in half and half. Add to the mixture in skillet, along with the cheeses. Cook and stir over medium heat until thickened and bubbly. Spoon cream cheese mixture over rings. If desired, sprinkle with slivered almonds.
Bake, covered, at 325°F for 35 minutes or until heated through.