Thaw puff pastry according to package directions. Preheat oven to 400 degrees.
Roll out the first puff pastry sheet into a larger rectangle. Spread half of the apple butter onto the surface.
Cut the brie into small cubes. Arrange half of the brie on top of the apple butter.
Fold the puff pastry sheet from short end to short end. Slice 1" strips from long end to long end. Starting in the middle of a pastry strip, twist the dough out to the ends. Place twists on parchment lined baking sheet. Repeat with the second sheet of puff pastry.
Whisk the egg with 1 Tbsp. of water. Brush the twists with egg wash.
Combine the rosemary and sugar in a small bowl. Sprinkle the twists generously with rosemary sugar.
Bake 20 minutes. Cool to room temperature before serving.