Blanch spinach in saucepan of boiling water 1 minute. Drain in sieve; press to extract all moisture. Combine spinach, Swiss and ricotta cheeses, nutmeg, salt and pepper in small bowl.
Lay out 6 wonton wrappers on clean, dry surface. Fill and fold wonton wrappers. Place each finished dumpling on a baking sheet. Cover with a damp cloth. Continue until you have 36 dumplings. The dumplings may be frozen, separated between layers of waxed paper, in a plastic bag or container for several weeks or refrigerated for up to 12 hours.
Bring a pot of salted water to boiling.
Melt butter in large skillet over medium-high heat. Add shallots; cook 2 minutes, until softened. Add mushrooms; cook until moisture is released, 7 minutes. Add vinegar and half the parsley; cook until vinegar is almost completely evaporated, about another 3 minutes. Reduce heat to low; simmer to thicken, 5 minutes.
Cook dumplings in boiling water for 2 to 3 minutes or until they rise to the surface. (Frozen dumplings will take 5 minutes.) Remove dumplings with slotted spoon to a platter or individual plates. Add half-and-half and salt and pepper to skillet with mushrooms; heat through. Pour sauce over the dumplings. Sprinkle with remaining parsley. Serve immediately. Makes 6 servings.