Preheat oven to 500 degrees. Follow procedure for pizza dough.

Melt 2 tablespoons butter with 1 tablespoons olive oil in heavy large skillet over medium heat. Add onions and a pinch of kosher salt (affiliate link) and sauté until golden, tossing frequently about 35 minutes. Season with salt and pepper. Set aside.

Melt remaining 2 tablespoons butter with 1 teaspoon olive oil in the same skillet over medium-high heat. Add mushrooms, garlic, and shallot. Sauté about 10-15 minutes until golden**. Add wine and simmer until almost all liquid is absorbed, stirring frequently, about 13 minutes. Add rosemary; season with salt and pepper.

Top 1/4 onion mixture on each crust, arrange 1/4 mushroom mixture on top of onions and top with Fontina cheese. Drizzle more olive oil on top of pizza. Pepper to taste.

Follow instruction for pizza dough on cooking. Be sure to use parchment paper (affiliate link) as instructed in the pizza dough recipe, it helps it slide off the cookie sheet onto the preheated cookie sheet. Bake for approximately 12 minutes, until crust is crispy and cheese is golden.

*be sure to buy Italian style Fontina vs. Danish Fontina. The Danish variety is too mild and soft for the flavors of this pizza. Goat cheese would be a good substitute.

** mushrooms go through ‘phases’ while cooking, pay attention to them, at first, they will suck up all the butter and oil in the pan, that’s a-okay. Next, they will exude a ton of moisture, that’s good too, but you’re not done yet. Let that exuded liquid evaporate and then the mushrooms will get nicely browned, then and only then, add the wine and scrape up any bits on the bottom of the pan with a flat wooden spoon.

• The onions and mushrooms can be prepared a day to two ahead of time.
• Brown button mushrooms will work just fine in this recipe, but wild mushrooms have a bit more deep flavor, and they have pretty shapes when sliced!