Preheat oven to 350° F.
Wash the zucchini and yellow squash in cold water, then dry. Slice off the ends (stem and blossom) of each zucchini and squash and discard. Slice the remaining zucchini and squash into 1/2" rounds.
Fill large stock pot with 3"of water.
Place an expandable steamer basket in Stock pot. The water line should be below the steamer basket.
Place zucchini and squash rounds in the steam basket.
Cover the pot and steam zucchini and squash for 10 minutes. You will see the centers begin to turn opaque (shiny and transparent).
After the zucchini and squash are steamed strain them in a colander.
Place the steamed zucchini and squash in a 9" x 13" baking dish.
Sprinkle the shedded cheese over the zucchini and squash and toss gently. You will see the cheese begin to melt over the hot zucchini and squash.
In a separate bowl mix together the cream of celery soup and the sour cream.
Add the soup and sour cream mixture to the zucchini and squash, stir to coat the vegetables.
In the microwave or on the stove top melt the butter.
Place the dry stuffing in a large bowl and add the butter. Toss to mix.
Spread the stuffing mixture over the top of the casserole.
Cover with tin foil and place in the oven for 30 minutes.
After 30 minutes, remove the tin foil and leave in the oven for an additional 5 minutes. Remove from oven and serve hot.