Heat oven to 425° F. Heat 1 teaspoon of the oil in a large skillet over medium-high heat.
Add the beef and cook, breaking it up with the back of a spoon, until no longer pink, 4 to 5 minutes. Stir in the barbecue sauce.
Oil a 10-inch ovenproof skillet and press the pizza dough into the bottom and up the sides.
Top the dough with the beef and sprinkle with the cheese. Bake until golden brown, 20 to 25 minutes.
Top with the arugula, tomato, and onion. Drizzle with oil and sprinkle with a pinch each of salt and pepper.