Whisk the warm water, yeast, and granulated sugar together in the bowl of your stand mixer fitted with a dough hook or paddle attachment. Cover and allow to rest for 5 minutes. 
*If you don’t have a stand mixer, simply use a large mixing bowl and mix the dough with a wooden spoon or rubber spatula in the next step.

Add the olive oil, salt, and flour. Beat on low speed for 2 minutes. Turn the dough out onto a lightly floured surface. 

With lightly floured hands, knead the dough for 5 minutes (for a visual, watch me do it in the video above). The
dough can be a little too heavy for a mixer to knead it, but you can certainly use the mixer on low speed instead. 

After kneading, the dough should still feel a little soft. Poke it with your finger – if it slowly bounces back, your
dough is ready to rise. If not, keep kneading.

Lightly grease a large bowl with oil or nonstick spray– just use the same bowl you used for the dough. Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl with aluminum foil, plastic wrap, or a clean
kitchen towel. Allow the dough to rise at room temperature for 60-90 minutes or until double in size. (Tip: For the warm environment on a particularly cold day, heat your oven to 150°F (66°C). Turn the oven off, place the dough
inside, and keep the door slightly ajar. This will be a warm environment for your dough to rise. After about 30 minutes, close the oven door to trap the air
inside with the rising dough. When it’s doubled in size, remove from the oven.)

Preheat: Place a pizza stone (if you have one) in the oven. Preheat oven and pan to 500°F (260°C).

Cook Mushrooms: In a large sauté pan, heat 1 tablespoon of the oil over medium heat. Add sliced mushrooms, cooking until mushrooms sweat out their moisture and begin to turn golden brown and crispy, about 10 minutes.

Assemble: Roll out pizza dough onto parchment paper, brushing the top with remaining 1 tablespoon of oil. Sprinkle with cheeses, then top with your cooked mushrooms and olives. Carefully slide the parchment paper and pizza onto your preheated pizza pan, then bake for 10 to 12 minutes, or until crust is golden brown.

Serve: Drizzle truffle oil over pizza right before serving, optionally topping with thinly grated fresh truffle.