Preheat oven to 400°F. Place flatbread on a parchment-lined baking sheet.
In a skillet over medium heat, warm olive oil. Add sliced onion and cook, stirring occasionally, until deeply caramelized (about 20–25 minutes).
Spread caramelized onions evenly over the flatbread. Layer with pear slices, gorgonzola, mozzarella, and thyme.
Bake for 10–12 minutes, until cheese is melted and bubbly.
Remove from oven and top with toasted walnuts, a drizzle of honey, and a handful of fresh arugula.
Slice and serve warm.