When the dough has about a half hour left to rise, begin prepping fillings. Cut the florets off the broccoli and slice the mushrooms. Mince or press the garlic cloves.
Also, this is a good time to preheat the pizza stone, with a sprinkling of corn meal on top, in the oven at 450°.
In a large skillet, combine the vegetables and garlic, along with a drizzle of olive oil. Cook until the vegetables are soft.
Combine the cheeses and vegetable fillings in a bowl. Mix to combine evenly.