Arrange a rack in the upper third of the oven and heat the oven to 400°F.

Trim 2 pounds zucchini and cut crosswise into ¼-inch thick rounds. Place in a large bowl, sprinkle with 1 teaspoon of the kosher salt, and toss to combine. Let sit for 10 minutes.

Meanwhile, mince 4 garlic cloves. Finely grate 1 ounce Parmesan cheese (about ½ cup lightly packed) if needed, or measure out ⅓ cup store-bought grated. Grate 4 ounces low-moisture mozzarella cheese on the large holes of a box grater, or measure out 1 cup store-bought shredded.

Melt 2 tablespoons unsalted butter in a large ovenproof or cast iron skillet over medium heat. Add the garlic and cook until fragrant, about 30 seconds. Add ½ cup heavy cream, ½ cup sour cream, 1 ½ teaspoons Italian seasoning, ¼ teaspoon black pepper, the remaining ¼ teaspoon kosher salt, and half of the Parmesan and mozzarella cheeses. Stir until the cheeses are melted, about 1 minute. Remove the pan from the heat.

Arrange the zucchini in a single layer on a double layer of paper towels or kitchen towel. Pat dry with more paper towels or another kitchen towel. Wipe out any accumulated liquid or remaining salt with a paper towel from the bowl.

Return the zucchini to the bowl, add the cheese sauce, and stir to coat the zucchini. Return to the skillet and spread into an even layer. Sprinkle with the remaining Parmesan and mozzarella cheeses.

Bake until the top is golden brown and the zucchini are tender, 20 to 22 minutes. Place on a wire rack and let cool for 5 minutes before serving.