01 -
Warm olive oil and butter in a large skillet over medium-low heat. Add sliced onions and cook slowly for 25 to 30 minutes, stirring occasionally, until onions become deep golden brown and very soft.
02 -
Stir in balsamic vinegar, thyme, salt, and pepper. Cook for an additional 2 minutes, then remove from skillet and set aside to cool.
03 -
In the same skillet, add a drizzle of olive oil if needed and cook sliced mushrooms over medium-high heat for about 5 to 7 minutes until golden and all moisture evaporates.
04 -
Add minced garlic to the mushrooms and sauté for 30 seconds. Remove from heat and mix mushrooms with caramelized onions. Let the filling cool slightly.
05 -
Preheat oven to 400°F. Roll out the thawed puff pastry on a sheet of parchment paper.
06 -
Position the pastry so the long side faces you. Spoon onion-mushroom mixture down the center third of the pastry, leaving sides clear. Scatter shredded cheese evenly over the filling.
07 -
Cut 1-inch wide diagonal strips along both sides of the pastry. Alternately fold strips over the filling from each side to create a braid pattern.
08 -
Brush the top of the pastry with beaten egg. Sprinkle with sesame seeds if desired.
09 -
Transfer with parchment to a baking sheet. Bake for 25 to 30 minutes, or until pastry is golden brown and puffed.
10 -
Allow to cool for 5 minutes. Garnish with fresh thyme leaves. Slice and serve warm.