Make the pizza dough. Add the flours, salt, and instant yeast to a bowl and whisk to combine. Add the water and stir with a rubber spatula until a sticky dough forms. Cover with a damp kitchen towel or plastic wrap and set aside to rise until doubled in bulk—1 to 1 1/2 hours.
Meanwhile, make the BBQ sauce and grill the chicken.
First, get your grill going. For charcoal: Set up for one-zone, high-temp cooking. For gas: Heat to high until the temperature reaches about 600° F. Make sure the grill grates are clean, then grease them with a lightly oiled cloth.
While that’s heating up, make the BBQ sauce. Combine the ketchup, cider vinegar, and chipotles in a food processor. Buzz until smooth. Season with salt and adobo sauce to taste.
Now grill the chicken. Rub with the vegetable oil and season with salt. Grill until charred and cooked through, 4 to 5 minutes per side. Let rest.
Whoa, your pizza dough has doubled in size! Great. Divide in half and use floury hands to roll each into a ball. Let rest for 20 or so minutes.
Meanwhile, chop the chicken into chunks and toss with a big plop of BBQ sauce.
Grilled pizza time! Bring the pizza dough blobs to the grill, along with a big cutting board. Use floury hands and as much extra flour as needed to stretch one dough ball into a 10-inch circle. It doesn’t have to be perfect. Mine turned out closer to rectangles and—guess what—they still tasted as good. Drape onto the the grill grates (if it’s gotten a little weird along the way, you can quickly reshape). Grill for 2 to 3 minutes (covered, if you’re using a gas grill). Transfer to the cutting board, un-grilled side facing down. Repeat with the remaining dough ball.
Top the pizzas in this order: mozzarella and gouda, then chicken and onions, dividing the toppings evenly between each pizza. Drizzle both with some more BBQ sauce. Return to the grill and cook another 3 or so minutes, covered, until the cheese has melted.
Remove the pizzas to the cutting board and top with the cilantro. Let cool a few minutes, then cut into pieces.
Emma is a writer and recipe developer at Food52. Before this, she worked a lot of odd jobs, all at the same time. Think: stir-frying noodles "on the fly," baking dozens of pastries at 3 a.m., reviewing restaurants, and writing articles about everything from how to use leftover mashed potatoes to the history of pies in North Carolina. Now she lives in Maplewood, New Jersey with her husband and their cat, Butter. Stay tuned every Tuesday for Emma's cooking column, Big Little Recipes, all about big flavor and little ingredient lists. And see what she's up to on Instagram and Twitter at @emmalaperruque.