Preheat oven to 400F degrees. Melt 2 Tablespoons butter, 1 Tablespoon oil in a 12-inch non-stick skillet or well seasoned cast iron skillet over medium heat. Add 1 Tablespoon thyme and about 5 slices of the onion (reserve the remaining slices), placed equally around bottom of the skillet. Cook for 5 minutes, until onion begins to soften. Do not stir. You are making a design for the top of the tart.
In a large bowl, place the sliced potatoes, 2 Tablespoons olive oil, ¾ cup Parmesan, ¾ cup feta, ¾ cup mozzarella, 1-2 minced garlic, 1 teaspoon salt and 1 teaspoon pepper. Toss to combine.
You should have several slices of the onion left. Chop these and add to the potato mixture. Mix again.
Layer the potato slices on top of the onion slices and continue in layers until the pan is full. You may need to add the cheese that doesn't adhere to the potatoes between the layers as you go.
Cover the skillet with aluminum foil and bake in oven for 20 minutes.
Remove aluminum foil and bake an additional 20-25 minutes, until the potatoes are golden.
Take skillet out of the oven and let rest for 10 minutes.
Using a serving plate that is larger than the diameter of the skillet, carefully invert the tart onto the plate (using hotpads). If some of the potatoes and/or onion sticks to the skillet, no worries - just scrape them off using a spatula and place back where they belong on the tart.
Sprinkle with additional thyme leaves and black pepper.