Preheat the oven to 375°F (190°C/Gas Mark 5) and line a baking sheet with parchment paper.
Cook the onion in a skillet over low heat with the olive oil and a pinch of salt until translucent. Stir in the honey, increase the heat to medium, and let caramelize for 3–4 minutes. Remove from the heat.
Peel, core, and thinly slice the apple.
Cut the Brie into 6 equal pieces.
Cut the puff pastry into 6 equal rectangles and set on the prepared baking sheet.
Place a small mound of caramelized onion in the center of the left-hand side of each rectangle. Divide the apple slices over the onions, followed by the Brie. Top the filling in each pastry rectangle with a pinch of fennel seeds and the leaves from a half-sprig of thyme (use the stems, too, if they are tender). Set aside a few thyme leaves for sprinkling over the turnovers.
To close the turnovers, fold the right-hand side of each rectangle over the filling on the left. Press around the edges with the tines of a fork to seal well.
Brush the pastry with the egg yolk and sprinkle with the remaining thyme leaves, salt, and pepper.
Bake for 15 minutes, until golden brown. Let rest for 5 minutes before serving.