For the dough, combine the water, yeast, sugar and olive oil and let stand for 5 minutes until foamy. In a large bowl, mix together both flours and salt. Add the wet ingredients to the dry ingredients and stir until it forms a shaggy dough. Turn the dough onto a lightly floured work surface and knead for 10 minutes until the dough is smooth and elastic. (Alternatively, the dough can be mixed in the bowl of a stand mixer using a dough hook.)

Gather the dough into a ball, transfer to an oiled bowl and cover. Place the bowl in a warm spot to allow the dough to rise until it has doubled in size, about 2 hours.

For the mushrooms, whisk together 3 tablespoons olive oil, balsamic vinegar, salt and pepper in a large bowl. Add the mushrooms, tossing to coat.

Rub the corn with 1/2 teaspoon olive oil.

Preheat a gas or charcoal grill on high heat.

Grill the corn until it's lightly charred, about 5-7 minutes. Let the corn cool slightly before slicing the kernels off the cob.

Grill the mushrooms until they are grill marked, about 1-2 minutes per side.

On a lightly floured work surface, roll out the dough into a 12-inch diameter circle. Place the dough directly on the grates and grill for 3 minutes with the lid closed until the crust has grill marks and has puffed up. Turn over the crust and grill for an additional 2 minutes.

Sprinkle the mozzarella over the pizza. Continue grilling until the cheese has mostly melted, about 2-3 minutes. Top with corn, mushrooms and garlic. Grill for another minute or so to warm the toppings.

To finish, sprinkle the pizza with chives and shaved Parmesan and season to taste with flaky sea salt and black pepper.