01 - Preheat oven to 475°F and place a pizza stone or heavy baking sheet inside to heat.
02 - Melt butter with olive oil in a large skillet over medium heat. Add onions, salt, and sugar. Cook, stirring occasionally, for 20-25 minutes until deeply golden and caramelized. Stir in black pepper and balsamic vinegar. Remove from heat.
03 - On a lightly floured surface, stretch or roll dough into a 12-inch circle. Transfer to parchment paper.
04 - Brush dough lightly with olive oil. Evenly spread 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 pizza with parchment onto preheated stone or baking sheet. Bake for 12-15 minutes until crust is golden and cheese is bubbling and lightly browned.
07 - Remove from oven and cool for 2 minutes. Garnish with fresh arugula or basil if desired. Slice and serve immediately.