For pastry:

Combine flour and salt in processor. Add oil, 2 Tbsp egg (reserve remaining egg for filling) and 3 Tbsp water. Process until smooth dough forms, adding more water by teaspoonfuls if dough is dry. Turn dough out onto lightly floured surface and knead until smooth, about 1 minute. Wrap dough in plastic and let stand 30 minutes.

Meanwhile, prepare filling:

Heat 1½-tsp olive oil in heavy medium skillet over medium heat. Add onion and leek and sauté until tender and golden, about 4 minutes. Add chard, spinach and oregano and sauté until very tender, about 10 minutes. Transfer to small bowl. Mix in cheeses. Season with salt and pepper. Mix in 1 Tbsp egg reserved from pastry. Set filling aside to cool.

Line large baking sheet with foil. Roll out dough on floured surface to generous ¹/₁₆-inch thickness. Using floured 2- to 2½ inch round cutter, cut out rounds. Gather dough and re-roll, cutting out more rounds for a total of 24.

Place 1 tsp filling in center of each dough-round. Brush edges of rounds with egg white. Fold dough over, forming half-circle, and press edges to seal. Place pastries on prepared baking sheet. (Can be made 1 week ahead. Cover and freeze. Thaw before continuing, and pat dry if dough is wet).

Pour vegetable oil into heavy large Dutch oven to depth of 1½ inches. Heat oil to 375°F. Working in batches, fry pastries until brown and crisp, about 5 minutes. Using slotted spoon, transfer pastries to paper towels and drain. Arrange pastries on platter. Serve warm or at room temperature.