To make the pickled onions, put the onion in a small saucepan and pour the boiling water over them. Let sit for 5 minutes, then drain and rinse well. Combine ½ cup vinegar, 1 tablespoon sugar, and ⅛ teaspoon salt in the saucepan and bring to a boil over medium-high heat. Add the blanched onion and stir to combine, then transfer to a pint-sized jar and set aside to cool to room temperature.
To make the pickled jalapenos, in the same saucepan, combine the remaining ¾ cup vinegar, 1½ tablespoons sugar, and ⅛ teaspoon salt. Add ¼ cup water and bring to a boil over medium-high heat. Add the sliced jalapenos and remove from the heat. Set aside for 10 minutes. Transfer to transfer to a pint-sized jar and set aside to cool to room temperature. The pickles can be covered and refrigerated for up to 1 week.
When ready to make the pizzas, remove the grates on your Spark and place the pizza stone directly over the heat spreader. Preheat the grill to 850°F.*
When the grill is preheated, on a lightly floured surface, stretch one 8-oz piece of dough into a thin round. Carefully transfer the dough to a flour- or cornmeal-dusted metal pizza peel.
Top the dough evenly with half of the shredded cheese and sliced mushrooms. Drizzle with 2–3 tablespoons of the sauce.
Carefully slide the pizza onto the hot pizza stone and close the lid of the grill. Bake on the stone for 1–2 minutes or until the bottom is set and starting to brown (watch carefully, checking about every 30 seconds so it doesn’t burn). Slide the peel under the pizza and lift it up slightly at an angle to finish cooking and browning, 1–2 more minutes.
Slide the pizza onto a cutting board. Top with the pickled onions and jalapenos, and garnish with cilantro. Cut into wedges and serve right away.
*To prevent burning, if the stone gets too hot after the first pizza, reduce the heat to 750°F and scrape any blackened bits from the stone. Repeat to use the remaining dough.