MELT butter in a large frying pan over medium. Add sliced apples, onion and salt. Cook, stirring occasionally, until onions are golden, 15 to 20 min. Stir in cider vinegar thyme leaves. Season with fresh pepper.
UNROLL puff pastry onto a parchment-lined baking sheet. Use a paring knife to score a 1-in. border around pastry square. With a fork, prick holes all over pastry. Sprinkle with crumbled goat cheese, then cover with apple mixture. Brush egg over apples.
BAKE in bottom third of oven until pastry is golden brown, about 25 min.