Leek and Olive Tart with Two Cheeses

to 20 baby leeks or 3 large leeks, white and pale-green parts only

unsalted butter

extra-virgin olive oil

Coarse salt

finely chopped fresh thyme

box (14 ounces) frozen puff pastry, such as Dufour, thawed

large egg beaten with 1 tablespoon water

freshly grated Parmesan cheese

Scant 1/4 cup Nicoise olives, pitted

Pave d'Affinois or other soft-ripened cheese (such as Camembert or Perail), thinly sliced