Add 355 g bread flour, 80 g whole wheat flour, 10 g granulated sugar, and 1/2 teaspoon instant or rapid rise yeast to a food processor and pulse until combined.
Turn on the food processor and slowly pour in 320 ml ice water while the processor is mixing. Once the water has all been added, keep processing until all the flour is incorporated and the dough forms a sticky ball (about 1 minute). Let it rest in the food processor for 10 minutes.
Sprinkle 10 g kosher salt over the dough, then turn on the food processor and stream in 15 ml olive oil. Continue to process until the dough forms a smooth ball (about 30-60 seconds).
Remove the dough from the processor, and knead on a lightly oiled countertop a few times just to form a ball. Place into a medium oiled bowl and cover with an air tight lid or plastic wrap. Refrigerate for at least 24 hours or up to 3 days (see note).
For the toppings
Heat oil in medium skillet over medium heat. Add the sliced mushrooms and sauté until golden brown, 10-15 minutes. Season to taste with salt and pepper. Transfer to a plate or bowl. They can be refrigerated until needed.
Turn skillet to medium-low heat and add 2 Tablespoons of olive oil. Sauté the sliced onions until soft and golden brown. If the onions become dry and start to brown to quickly, add 1-2 Tablespoon of water to the pan. Transfer to a bowl or plate and refrigerate if needed until you're ready to use them.
Place a pizza stone on the middle rack of the oven and preheat to 500°F for one hour.
Cut the dough into four pieces. Work with one piece at a time and the the others covered. Roll and/or stretch into a circle. Lay on a wooden cutting board, pizza peel or rimless baking sheet that has been covered with cornmeal or semolina. Lightly brush with olive oil and cover with the onions, mushrooms, and crumbled goat cheese. Add freshly ground pepper if desired.
Transfer pizza to the pizza stone in the oven. Bake until crust and cheese are starting to brown, 10-15 minutes.
Remove from oven and cut into wedges.
Notes
If you need your pizza dough sooner, simply increase the yeast. Use 1 ½ teaspoons for dough that only needs to rise 1-2 hours.