Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.

On a lightly floured surface, roll out the brioche dough into a circle approximately 11 inches in diameter.

Arrange the prosciutto slices in the center of the dough in an overlapping pattern to create a bed for the cheese.

Place the wheel of Brie on top of the prosciutto stack.

In a small bowl, mix the honey, red pepper flakes, and half of the fresh thyme leaves.

Drizzle the spicy honey mixture directly over the top of the Brie wheel.

Gently fold the edges of the brioche dough up and over the cheese, pleating it as you go to seal the Brie completely inside. Pinch any seams tightly to prevent leaking.

Flip the wrapped bundle over so the seam side is down and place it on the prepared baking sheet.

Whisk the egg with 1 tablespoon of water to create an egg wash, then brush it over the entire surface of the dough.

Bake for 20 to 25 minutes, or until the brioche is a deep golden brown and sounds hollow when tapped.

Allow the baked brie to rest for at least 10 minutes before cutting; this ensures the cheese doesn't run out too quickly.

Garnish with the remaining fresh thyme and serve warm.