Making a literal thousand-layer cake?
I don't know what kind of thousand layer cake you had in the restaurant but only ten layers don't sound like it was a Mille-feuille ("a thousand leaves"). A Mille-feuille is a french pastry that consists of three layers of puff pastry, alternating with two layers of pastry cream. That's basically the same thing as your suggestion with phyllo dough. 

Assuming that one layer of puff pastry has about 80 layers, you "only" need to stack about 12 or 13 layers puff pastry (puff pastry is something ordinary in the groceries store, so you don't even have to make your own puff pastry). If you put some (butter) cream / custard / jam / whatever between each layer 12 layers should be sufficent. Voilà! A real Mille-feuille :) It's ~4 times taller than a regular Mille-feuille but certainly lower than 1000 or 500 stacked crêpes.