Place olive oil in a large sauce pan over medium heat. Add onions and cook, stirring occasionally, until caramelized, about 35 minutes. Season with salt. Let come to room temperature.

While onions are cooling, place goat cheese in a small bowl. Add black pepper and stir goat cheese until soft and easily spreadable.

Preheat oven to 375°F. Line a baking sheet with parchment paper.

Place puff pastry on baking sheet. Spread goat cheese over tart, leaving a ½ inch border on all sides. Top tart evenly with onions and sprinkle with thyme. Bake until crust is golden, about 25-30 minutes.

Let tart cool for 15 minutes. Cut into approximately 2 by 3 inch rectangles. Serve warm or at room temperature.