Toss zucchini slices with 1 tablespoon kosher salt in a colander set over a bowl. Let drain for 15 minutes - this draws out excess water so your gratin doesn't turn soupy. Pat very dry with clean kitchen towels.

In a large skillet, combine heavy cream, minced garlic, nutmeg, and black pepper. Bring to a gentle simmer over medium heat and cook for 3 minutes until slightly thickened and fragrant. Remove from heat.

Preheat oven to 400 degrees F. Grease a 9x9 inch baking dish with softened butter. Arrange half the zucchini slices in overlapping layers, pour over half the cream mixture, and sprinkle with half the gruyere. Repeat with remaining zucchini, cream, and gruyere. Top with parmesan.

Bake uncovered for 30-35 minutes until the top is deeply golden and the cream is bubbling around the edges. Let rest 10 minutes before serving - this allows the sauce to set so you can cut clean squares.