Cook zucchini, onion and carrots in water until tender (about 15 minutes). Drain. Add the mayonnaise and undulated soup and set aside.
In a separate saucepan, melt butter and add the Stove Top stuffing mix. Butter a 2-quart casserole dish. Layer one half of the zucchini mixture and the rest of the stuffing mixture.
Bake in a preheated 350 degrees oven for about 45 minutes until the top is lightly browned and the casserole is nice and bubbly.