Preheat oven to 350°F (177°C). Line a baking sheet with parchement paper and set aside.
Using a sharp knife, score the top rind of cheese in a criss-cross pattern, spacing cuts about 1 inch apart.
Roll puff pastry sheet out onto a large cutting board or work surface dusted with flour. Set cheese wheel in the center of the square, and top with 2-3 tablespoons of fig spread. Sprinkle thyme leaves on top.
Fold dough up and over the sides of cheese, pleating it on top to enclose the cheese wheel. Gently pinch dough together in the center to seal gathered pleats. You can tie a bit of kitchen twine on top to hold pleats together if you like, but this is not required.
If the dough is no longer cold after assembling, chill wrapped cheese for at least 20 minutes before baking. Prepared cheese wheel can be wrapped tightly with plastic wrap and refrigerated until ready to bake.
Place wrapped cheese wheel on prepared baking sheet and brush evenly with egg wash. Bake until puff pastry is crisp and golden brown all over, about 25 to 35 minutes. Let baked brie rest for 5 minutes, then transfer to a round serving board. Garnish with sliced figs and rosemary sprigs if desired. Enjoy!