Prepare pastry:
Preheat oven to 400°F.
Unfold pastry sheet on a greased baking sheet, then turn over (to prevent creases from splitting during baking). Trim edges with a sharp knife. Brush pastry lightly with egg (do not allow to drip down sides). Create a 3/4-inch border all around by lightly scoring a line parallel to each edge of pastry (do not cut all the way through). Prick inner rectangle evenly with a fork, then sprinkle with 1 tablespoon sugar.
Bake in lower third of oven 15 minutes, or until puffed and golden brown. Transfer to a rack and cool to room temperature.
Make cream and cut mangoes while pastry bakes and cools:
Whisk together sour cream, cream cheese, remaining 3 tablespoons sugar, and zest.
Thinly slice mangoes lengthwise with a mandoline or other manual slicer or a sharp knife (be careful because peeled mango is slippery), then halve wide slices lengthwise.
Assemble tart:
Just before serving, spread cream over inner rectangle of pastry and top with mangoes, folding decoratively.
