If using store bought pizza dough, allow to come to room temperature.
Heat 1 tablespoon olive oil in skillet over medium heat. Add sliced mushrooms. Stir to coat mushrooms in oil. Cook for 2-3 minutes until mushrooms start to release moisture. Add 1 tablespoon soy sauce and continue to cook until all liquid is absorbed and mushrooms are soft. Stir frequently. Season with back pepper, if desired. Transfer mushrooms to clean bowl and set aside until ready to use.
Heat 1/2 tablespoon olive oil in skillet. Add torn kale leaves. Toss to coat kale in oil. Sauté kale for about 90 seconds, just until kale begins to wilt. Remove from heat and set aside until ready to use.
Preheat oven to 475 degrees F.
Spread remaining 1 tablespoon olive in a 12-inch cast iron skillet. Place room temperature pizza dough in oiled skillet. Using your hands, gently push and pull dough to fit skillet.
Spread 2-3 tablespoons of pesto on pizza dough, leaving about 1/2-inch border around the perimeter of pizza. Sprinkle mozzarella and fontina over pesto. Arrange cooked mushrooms and kale over cheese.
Transfer skillet to stove and set over medium-high heat. Warm up the skillet. Cook the pizza for about 3 minutes until the bottom of the crust has set and the oil is bubbling along the outer rim of the pizza.
Transfer hot skillet into preheated oven. Bake for 7-10 minutes until the cheese has melted.
Remove from the oven and let sit for 2-4 minutes before unmolding pizza. Add sliced prosciutto. Place pizza on cutting board and use a sharp knife or pizza wheel to cut into slices.