1. Heat oil in a heavy-bottomed skillet. Add the onions and cook over medium heat for 30 to 40 minutes or until onions have caramelized and turned completely brown. Stir regularly while cooking to avoid burning. If onions begin sticking to the pan, deglaze with a little water and reduce the heat.
2. Add garlic and dried tomatoes to the onions for the last 10 minutes of cooking.
3. Meanwhile, oil the barbecue grill and preheat it for about 15 minutes on medium.
4. Remove onions from the heat and add olives to mixture. Salt and pepper to taste.
5. Place pizza crust directly on barbecue, side to be dressed face down, and grill 1 or 2 minutes.
6. Remove from the heat and spread the onion mixture evenly over the grilled side of the pizza. Sprinkle with oregano, and then top with shrimp.
7. Place directly on the barbecue grill. Close the lid so the heat will circulate around the pizza. Cook 2 or 3 minutes on medium until pizza is nice and crispy. Watch the pizza closely to make sure it doesn't burn.
8. Garnish with shaved Parmesan and arugula and serve immediately.

Original idea:
Cut the pizza into 12 bite-size slices to serve at cocktail hour.
A guaranteed hit!