Caramelize the onions by cooking them in a heavy skillet over medium heat with the olive oil until deep golden brown- about 30 minutes. Add thyme, season to taste with salt & pepper. (Can be done ahead and refrigerated-- come to room temperature before using)

Preheat oven to 375 degrees. Cut full puff pastry into 16 pieces and half-sheet into 8 pieces. Whisk egg with 1 tsp water and brush pastry with eggwash. Cook for 10-12 minutes, until puffed and golden.

Top each pastry with a spoonful of caramelized onion, apple slice(s) and cook for 10 minutes more.

Remove rind form brie and make 24 equal pieces, about 1/4-inch thick. Top each pastry with cheese and cook 2-3 minutes more, until cheese is melted.

Notes: Use a soft hole-y brie for better melting.
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