Preheat your oven to 475°F (245°C). If you have a pizza stone, place it in the oven while it heats.
In a large skillet, heat the olive oil over medium heat. Add the sliced onions and a pinch of salt. Cook, stirring frequently, for about 15-20 minutes until the onions are soft and golden brown. Stir in the balsamic vinegar and cook for an additional 2 minutes. Remove from heat and set aside.
If using store-bought dough, follow the package instructions for rolling out. On a floured surface, roll out the pizza dough into your desired shape (round or rectangular) and about ¼ inch thick.
Transfer the rolled dough to a pizza peel or baking sheet lined with parchment paper. Evenly spread the caramelized onions over the dough. Sprinkle the shredded mozzarella cheese and crumbled goat cheese on top. Finish with the thyme, and season with salt and pepper.
Carefully slide the pizza onto the hot pizza stone or place your baking sheet in the oven. Bake for 12-15 minutes, or until the crust is golden and the cheese is melted and bubbling.
Once baked, remove the pizza from the oven. Allow it to cool for a couple of minutes, then top with fresh arugula if desired.