For the crust, in a small bowl whisk together the yeast, ¼ cup of water, and a pinch of sugar. Let the mixture sit while you prepare the rest of the dough. Meanwhile, in the bowl of a stand mixer fitted with the bread hook attachment, combine 2 cups of bread flour, olive oil, salt, and remaining water. When the yeast becomes foamy, add it into the bowl with the flour. (If the yeast doesn't become foamy, it may be dead and you'll have to start over with new yeast.)
Mix the dough on medium speed until well-combined. If the dough is still sticking to the sides of the bowl after a minute or mixing, then add in more flour. Mix on medium-high speed for 4 minutes. Cover lightly with plastic wrap and let the dough rise in a warm, draft-free place until doubled in size, about 30 minutes.
Meanwhile, heat the oven to 425ºF.
In a large skillet, heat the remaining olive oil over medium heat. Add the onions to the pan along with a sprinkle of salt. Saute for 8-10 minutes, stirring every 2 minutes, until starting to caramelize and brown. Add a tablespoon of water to the pan and saute for another 3-4 minutes. Stir in the bell pepper slices and saute until tender and starting to brown, about 3-4 minutes. Stir in the chickpeas. Season to taste with salt and black pepper.
Grease a 12-inch oven-proof pan or cast-iron skillet. Spread the dough in the skillet so that it reaches the sides. Top with ⅓ cup of the barbecue sauce, spreading it around the dough and leaving a ½-inch edge for the crust. Top with the grated cheese and the vegetable chickpea mixture. Drizzle with 1-2 tablespoons of additional barbecue sauce, or to taste.
Put the pan in the oven and bake for 15 minutes or until the cheese is bubbling and the bottom of the dough is golden brown. Let cool for 5 minutes, then slice and serve.
To save time, you can always use storebought pizza dough to make this recipe! Just make sure it comes to room temperature before using it.
Additionally, this pizza can be made thin crust instead of deep dish by making it on a 14-inch pizza pan. In that case, bake at 500ºF for 10 minutes.