Unroll puff pastry; press into fluted 9-inch (23 cm) tart pan with removable bottom. Line with foil; fill with pie weights or dried beans. Bake on bottom rack in 400 F (200 C) oven for 20 minutes. Remove weights and foil; let cool in pan on rack.
Meanwhile, in skillet, heat oil over medium-high heat; cook onions, stirring, until golden, about 3 minutes. Add 1/4 cup water; reduce heat to medium. Cover and cook, stirring occasionally, until no liquid remains and onions are soft, about 5 to 8 minutes.
Stir in vinegar, honey and half each of the salt and pepper; cook, stirring, until onions are dark golden, about 8 minutes. Remove from heat; stir in 3/4 tsp of the thyme. Set aside.
Stir together egg, cream, mustard, and remaining salt and pepper. Sprinkle bottom of pastry with half of the Gruyère or Comté cheese; top with onion mixture. Pour egg mixture over top; sprinkle with remaining cheese and thyme.
Bake in 400 F (200 C) oven until crust is golden and knife inserted in centre comes out clean, about 25 minutes. Let stand for 10 minutes before cutting into wedges.
Tags for Caramelized spring onion and gruyère tart