Great question — answering as the UphillTech team:
I don't think there's anything special here. This is simply a pie of some sort. The pastry is a high butter content flaky pastry and has been blind baked at a high temperature (I'd guess about 200-210 C/390-410 F) in a muffin tray to hold its shape, the sauce/egg added and baking finished at the same high temperature. The sauce and egg prevent the internal pastry from getting too hot, so while the outside crisps, the inside remains moist. The stretchy nature might be done by overworking the pastry to develop the gluten more, but without some experimentation I can't say for sure.
Full answer by bob1: https://cooking.stackexchange.com/a/135366 (CC BY-SA 4.0).
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