Remove tomatoes from water. Discard water.
Squeeze as much water out of tomatoes as you can.
Slice tomatoes into fine strips. Set aside on a paper towel-covered plate to absorb the rest of the water.
Clean mushrooms and slice into 1/4-inch pieces.
Add mayonnaise, sour cream 1/2 cup Asiago Cheese, green onion (except those few pieces reserved for garnishing) and mushrooms in food processor. Blend well at low speed.
Pour mixture into a mixing bowl.
Add tomatoes. Gently mix, by hand, until mixed well.
Spoon mixture into a microwave and oven-safe serving dish. Store, covered, in the refrigerator, until ready to serve.
When ready to serve, preheat broiler.
Place dish in microwave and heat through.
Carefully remove from microwave (dish will be hot).
Sprinkle with 1/4 cup Asiago cheese.
Put under the broiler and heat until cheese topping melts and browns.
Carefully remove from oven (dish will be very hot).
Serve hot (Be sure to warn your guests that it is very hot!) with toast points, pitas and other dippers.