Bring 5 cups water to a boil in a large pot. Slowly whisk in grits. Reduce heat and simmer, stirring often (grits will bubble in spots), until liquid has absorbed and grits are tender, 20 to 25 minutes. Remove from heat and season with salt; let stand for 5 minutes.
Preheat oven to 450°F. Lightly grease a baking sheet. Combine chicken and barbecue sauce in a bowl. Scrape grits onto baking sheet and spread out to form a 1/2-inch-thick oval; let stand for 5 minutes. Bake until warm, 4 to 6 minutes.
Remove from oven and switch oven to broil. Top grits with chicken, jalapeño (if desired), onion, and mozzarella. Broil, about 6 inches from heat, until beginning to brown, 2 to 3 minutes. Drizzle with barbecue sauce and sprinkle with cilantro.