Pre-heat oven to 425° F.
Melt butter in a heavy skillet (ie, Dutch oven) over medium heat.
Add apple and pear and cook, stirring often, until fruit is soft and releases some of its juices, about 5 minutes.
Add brown sugar and nutmeg and stir to combine.
Mix in lemon juice and cook, stirring occasionally, until liquid has thickened and become <g class="gr_ gr_86 gr-alert gr_gramm gr_inline_cards gr_run_anim Punctuation only-del replaceWithoutSep" id="86" data-gr-id="86">syrupy,</g> about 10 minutes.
Let cool to room temperature.
Place the puff pastry on a lightly floured surface and smooth with a rolling pin.
Roll out to roughly a 12" x 12" square. Transfer to rimmed baking sheet.
Place brie in the center of pastry and top with cooled fruit mixture.
Brush egg <g class="gr_ gr_83 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace" id="83" data-gr-id="83">wash</g> on the edges of the pastry.
Fold all 4 sides of pasty over cheese and firmly twist ends to create a seal at the top.
Brush all over with the egg wash.
Bake until deep golden, about 25 minutes.
Let rest 5 minutes before serving.