Preheat the oven to 425 degrees F. If using a pizza stone, heat the stone in the oven for 10 minutes.

Lay 2 pieces of naan on a pizza peel or on a baking sheet (if not using a pizza stone).

Heat 3 teaspoons of olive oil in a large nonstick skillet set over medium heat.

Add the onions, cover the pan and cook, stirring occasionally, until the onions are deep golden brown.

During the cooking, add water as necessary, 2 tablespoons at a time, to stop the onions from burning and drying out. Be sure that all of the water is absorbed before removing from the heat.

Season the onions with ⅛ teaspoon salt and the ground pepper. (For detailed pictures, see How to: Caramelize Onions). Transfer the onions to a bowl and set aside.

Increase the heat to medium-high and heat the remaining 1 teaspoon of olive oil in the skillet.

Add the mushrooms and cook, stirring occasionally, under the they are tender and starting to brown, 4 to 5 minutes.

Stir in the Marsala wine, fresh thyme and remaining ¼ teaspoon of salt, and cook until the liquid is absorbed. Remove from the heat.

Divide the fontina cheese evenly between the naan bread, then top with the caramelized onions, mushrooms and Parmesan cheese.

Transfer to the topped naan bread to the pizza stone (or place the baking sheet in the oven) and bake until the cheese is melted and the naan bread is golden brown, 7 to 8 minutes.

Transfer the pizzas to a cutting board and let rest for a few minutes before cutting.

Sprinkle the parsley over top. Slice the pizzas into quarters. Serve.