Combine the figs, orange zest, thyme, brandy, sugar, vinegar, a few grinds of pepper and 1/4 cup water in a small saucepan. Bring to a boil, then reduce the heat and simmer until the liquid is syrupy and the figs are softened, 15 to 20 minutes. Transfer to a small bowl, discard the zest and thyme and let cool, about 20 minutes. Transfer to a food processor or mini chopper and pulse until mostly smooth.
Preheat the oven to 375 degrees F. Unroll the pie dough onto a lightly floured work surface. Roll out the outer 2 inches of dough with a rolling pin to make the edge slightly thinner than the rest of the dough. Put the cheese in the center of the dough and top with the fig compote. Trim about 1 inch off the outer edge of the dough. Pull the dough up and over the cheese, folding and pleating the dough all the way around until the cheese is covered. Pinch the dough together at the top to seal.
Transfer the wrapped cheese to a parchment-lined baking sheet. Brush the dough with the beaten egg and bake until golden brown, 30 to 35 minutes. Let cool about 10 minutes, then transfer to a cutting board to slice. Serve warm or at room temperature.