carmelized onion tarte soleil

0 Slice the ends off the onions, then slice in half from root to stem. Peel, then thinly slice in the same direction.
1 Heat the oil and butter in a large skillet over medium heat until sizzling. Add the onions, salt, and thyme and cook, stirring, until beginning to brown, about 10 minutes. Reduce the heat to medium-low and cook, stirring every few minutes, until jammy and deeply golden, 25 to 30 minutes. (Add a splash of water if the onions stick).
2 Remove from the heat; discard thyme sprigs. Stir in balsamic and several grinds pepper.
3 While the onions cook, unfold one puff pastry sheet on a sheet of parchment paper. Find a round object ~11” wide (such as a Dutch oven lid); roll the pastry slightly larger. Trace around the lid, remove the excess dough, then transfer to the fridge. Repeat with the second sheet.
4 Brush the egg wash around the perimeter of one round. Spread with goat cheese, leaving a 1/2” border. Arrange the onions in a thin layer overtop (you may not need them all). Place the second round over top and press the edges to seal. Make an indent in the center with a small cup (~2” wide). Chill 15 minutes. 
5 Heat the oven to 375°F. Cut the pastry into 4 quadrants starting from the center circle. Cut each in half again, and again (you’ll have 16 strips total). Transfer to a baking sheet.
6 Gently twist each strand three times. Brush with egg wash and top with Parmesan. Bake until puffed and golden brown, 30 to 35 minutes. Drizzle with hot honey.