Prepare your pizza dough. When it has just 5-10 minutes of rising left, preheat outdoor bbq grill to medium-high heat. Place all other prepped ingredients on a tray so they're ready to go and easily accessible.
Divide dough into 4-6 pieces. Roll out each piece on a floured surface to about 1/3 of an inch thick. Lightly brush with oil.
Make sure grill grates are clean, and lightly grease them. (Tip: An easy way to grease grill grates is to dip a few folded paper towels in vegetable oil and use a pair of tongs to hold them and lightly rub them along grill grates.) Place dough oil-side down on grill. Lower heat just a bit and close the lid. Cook for a few minutes, checking for the dough to look puffed, and golden brown on the bottom. Lightly brush top side of dough and flip.
Immediately drizzle top of pizzas with bbq sauce and spread out evenly. Sprinkle with cheeses, pork, red onion, and pineapple. Close BBQ lid and cook for a few more minutes until crust is cooked and toppings are melted and bubbly and then sprinkle on cilantro or parsley. If bottom crust is getting too done, place on top rack, or turn off heat directly under pizza to let center of dough and toppings continue to cook. If needed, you can always pop pizzas under the broiler to brown tops.