Defrost sheet of puff pastry at room temperature for about 20 minutes. Preheat oven to 375°F. Unfold pastry.
Center Brie on pastry sheet. Spread jam over cheese. Sprinkle evenly with almonds. Bring corners of sheet together above Brie and twist gently to form a bundle. Tie gathered pastry at neck with kitchen twine. Chill in refrigerator for 15 minutes.
Place Witch's Purse on a parchment-lined baking sheet and brush lightly with beaten egg. Bake until pastry is golden all over, 25 to 30 minutes. Place on a platter garnished with fresh kumquats and grapes, if desired. Let sit 10 to 15 minutes before serving; let guests cut wedges.