Heat a skillet to med-high heat and coat the bottom of the skillet with 2 tablespoons of olive oil. Add the sliced onions and stir to coat the onions with the oil. Spread the onions out evenly over the pan and let cook, stirring occasionally.
After 10 minutes, sprinkle the salt and sugar over the onions. Let the onions cook for 20 minutes, stirring every few minutes, or until they become brown. Remove from heat and set aside.
Next, drizzle a 1 tablespoon of olive oil on the pizza crust and sprinkle with mozzarella cheese. Spread the caramelized onions, goat cheese, and black berries on top, and bake for about 15 minutes at 350 degrees F or until the pizza crust is golden brown.