Preheat oven to 400 degrees and line a baking sheet with parchment paper.
Heat olive oil in a pan over medium heat. Once hot, add the onions, garlic, and thyme and cook, stirring often, until brown and caramelized (about 15-20 minutes). Once caramelized, stir in the salt and remove from heat.
Roll the puff pastry sheet out to an approximately 20” by 10” rectangle. Transfer pastry sheet to prepared baking sheet and use a fork to prick holes in the dough, leaving about a 1” border around the edges (this will keep the dough in the center from rising).
Crumble the goat cheese evenly over the pricked portion of the dough, followed by an even layer of the caramelized onions. Arrange the tomatoes, cut side up, on top of the onions. Fold the edges of the dough in to meet the filling (so you’ll end up with about ½” border of double thickness dough around the edges of the tart).
Bake tart until edges are puffed and golden, about 20-25 minutes. Cool tart slightly, then sprinkle the top with fresh thyme leaves and flaky sea salt. Serve warm or at room temperature.