Make the dough:
In a large bowl, stir the warm water and sugar together, then sprinkle the yeast over it and let rest for 5 minutes; if it gets fluffy and frothy, you’re ready to move on. If not, it means you need to start again with new yeast, or with warm-but-not-hot water. (Too-hot water, like water that you don’t want your finger in, will kill the yeast.) Add 2 tablespoons of the olive oil, then add the salt and flour, and stir with a wooden spoon until a sticky but single piece of dough forms.
Lightly flour a clean workspace and scoop out the dough onto it. Knead the dough until smooth but not dry, adding flour by the tablespoonful if it’s too sticky to work with (you shouldn’t need much). Lightly oil a bowl, then transfer the dough to the bowl, cover with plastic wrap, and let rest in a warm place until the dough gets puffy, 40 minutes.
While the dough is rising, combine the chicken, barbecue sauce, sriracha, red onion, and cilantro in a bowl and gently mix to coat.
Preheat the oven to 425°F. Pour 2 tablespoons oil on the Cravings sheet pan, then place the dough on the center of the pan, flatten slightly, then use another tablespoon of oil to help you spread the dough into a 10-inch square. Preheat the Lowkey Lavender Grill Pan over medium, then brush with more oil. Move the crust in the baking sheet close to the grill pan, then use both hands to lift it from the baking sheet and arrange it in the grill pan, stretching it to the sides if necessary. Cook on the stove top until the crust is slightly browned and parbaked, 4 to 5 minutes.
Scatter the chicken and cheese evenly on top of the crust and carefully move to the oven to bake until the cheese is bubbling, 5-6 minutes. Remove from the oven and garnish with jalapeño and more cilantro. Transfer to a cutting board and use scissors of a pizza wheel to cut into squares. Serve hot.
