For the beef: In a large skillet, heat the oil over medium-high heat. Add the beef, sprinkle with salt and pepper and cook until the meat gets nice and golden brown, 10 to 12 minutes. With a slotted spoon, remove the beef and reserve. Lower the heat to medium and saute the onions in the beef juices until soft, about 5 minutes. Add the oregano and garlic and cook until fragrant, about 1 minute. Season to taste with salt and pepper. Add the tomato paste and cook until caramelized, 2 to 3 minutes. Deglaze with the red wine and scrape up any bits that have adhered to the pan. Add the beef back in, stir and set aside.
For the pizza: Preheat the oven to broil with the rack on the lowest position or heat a grill with one side on high and one side off for indirect heat. Scoop out some of the bread to create a well for the toppings. Brush all sides of the bread with olive oil. Top evenly with the beef mixture, then the mozzarella and feta, then top with the olives. Put on a baking sheet in the oven or place on the grill and cook until golden and bubbly, 5 to 8 minutes. Top with the Pickled Red Onions and fresh mint. Slice and serve.
Put the vinegar, sugar, salt and 1/2 cup water in a small pot and bring to a simmer. Add the onions and take off the heat immediately. Let cool and keep in an airtight container in the fridge for up to 2 weeks.