Slice off top half inch of tomatoes.
Scoop out pulp; chop it and the tops of tomatoes; put in colander to drain.
Shred zucchini and sprinkle with teaspoon salt; mix with tomato pulp; leave to drain for 1/2 hour.
Sprinkle inside of tomato shells with mixture of salt, sugar, and pepper.
Drain them upside down on paper towels in refrigerator for 1/2 hour or more.
Squeeze zucchini lightly; then saute in teflon skillet with tomato pulp, garlic, mushrooms, and oil for 5 minutes.
Turn up heat and stir constantly until all moisture is evaporated.
Season to taste with salt and pepper.
Cool mixture; chill for 1/2 hour or more.
Stuff tomato shells and garnish with mayonnaise and parsley.