Toss the zucchini with the salt and place in a wire mesh strainer or a colander with tiny holes. Allow the excess water to drip for about 10 minutes. Squeeze out the excess liquid with your hands. Alternatively, place the shreds in a thin dishtowel or cheesecloth and twist to squeeze out the juice.

When the zucchini is relatively dry, melt at least half of the butter in a skillet over medium heat. Sprinkle in the shreds of zucchini and spread out evenly in a saute pan. Sear for 2-3 minutes until it starts to become slightly golden. Flip over, spread out and sear again. Repeat this until the zucchini appears evenly cooked, adding more butter as needed.

Once the zucchini is relatively done, sprinkle on the swiss cheese. Cover and allow it to melt for about a minute. Drizzle in the cream and fold on itself to combine. Serve the cheese zucchini while it is still hot.

If planning to serve later, place in a small baking dish in a warm oven until ready to eat.