Coat a pizza baking sheet with nonstick cooking spray or olive oil. Roll the pizza dough so that it fits on the baking sheet. Brush 1 tsp of the olive oil over the top of the dough. Bake 5 to 7 minutes or until golden brown. Remove from oven and let cool.
For the caramelized onions, in a large skillet heat remaining 2 tsp olive oil over medium-high heat 1 minute or until hot. Add butter; melt. Add onions, thyme, and salt and pepper to taste.
Cook 5 to 8 minutes without stirring. Reduce heat to medium; stir in honey and vinegar. Cook another 15 to 20 minutes or until onions are caramelized, stirring occasionally. Remove skillet from heat and let it cool slightly.
Spread cream cheese over the top of the flatbread. Spread onions evenly over cheese. Cut into squares, sprinkle with parsley, and serve.