Heat 2 tbsp of olive oil in a large skillet over medium heat. Add onion and cook, stirring occasionally, until golden, about 10 minutes. Add in sliced mushrooms and sauté for an additional 10 minutes.
On a clean work surface, roll out pizza dough and place it on a large baking sheet or pizza stone. Brush dough with remaining 1 tbsp olive oil and a sprinkle of salt. Prebake for about 5 minutes or until golden brown; remove from the oven.
To top crust: Using a large spoon, spread the base of pizza with sweet potato puree and sautéed onions and mushrooms, and top with cheese. Place back in the oven on the middle rack for 10 to 12 more minutes, until dough is crisp and cooked through. Remove from oven, sprinkle with arugula and balsamic vinegar, and serve hot.