Preheat the oven to 350°F (177°C). Line a large baking sheet with a silicone baking mat or parchment paper and set aside.

In a small skillet or saucepan, melt the butter with the thyme. Pour into a heatproof bowl.

Lightly brush the silicone baking mat or parchment paper with a bit of the melted thyme butter. Unroll the phyllo dough sheets on a flat, dry surface. Remove the first sheet, then immediately cover the remaining phyllo sheets with a damp towel (or damp paper towels) to prevent them from drying out.

Lay a sheet of phyllo dough on the prepared baking sheet, and lightly brush it with melted thyme butter. Lay a second sheet of phyllo on top, rotated at about a 10-degree angle to the first one. Lightly brush it with the melted thyme butter, then repeat the layering of phyllo and brushing with butter, each time rotating the phyllo slightly until you’ve used all 10 sheets of phyllo dough. Cover the edges of the phyllo with damp paper towels as you work, to prevent the edges from drying out.

Spread the brie on top of the layered phyllo, leaving about a 4-inch border around the edges. If your brie isn’t spreadable, you can dot the phyllo with small pieces or slices of the brie instead.

Core and cut the apples into thin, even slices. In a medium bowl, toss the apple slices with the brown sugar until coated. Arrange the apples, overlapping slightly, on top of the brie.

Remove the damp towels and fold the edges of the phyllo over to make a crust edge around the apples, overlapping as needed. Brush the edges with remaining melted thyme butter.

Bake for 40–45 minutes, until the phyllo is golden brown and crisp.

Drizzle honey over the baked galette, and sprinkle with flaky sea salt and more fresh thyme, if desired. Slice and serve warm.

Cover and refrigerate leftovers for up to 3 days. Leftovers can be reheated in a 325°F (163°C) oven for around 10 minutes.