01 - Preheat oven to 475°F and place a pizza stone or heavy baking sheet inside to heat thoroughly.
02 - In a large skillet over medium heat, melt butter with olive oil. Add onions, salt, and sugar. Cook, stirring occasionally, for 20-25 minutes until onions are deeply golden and caramelized. Stir in black pepper and balsamic vinegar. Remove from heat and set aside.
03 - On a lightly floured surface, stretch or roll the pizza dough into a 12-inch circle. Transfer to a piece of parchment paper.
04 - Brush the dough lightly with olive oil. Evenly spread the caramelized onions over the base.
05 - Sprinkle mozzarella, fontina or Gruyère, and Parmesan cheeses over the onions. Top with thyme if using.
06 - Carefully slide the pizza with parchment onto the preheated stone or baking sheet. Bake for 12-15 minutes until the crust is golden and the cheese is bubbling and lightly browned.
07 - Remove from oven and let cool for 2 minutes. Garnish with fresh arugula or basil if desired. Slice and serve immediately.