In a medium bowl, combine the flour, baking powder, sugar, and salt.
Cut in 3 tablespoons (1½ oz/42 g) butter until the mixture is crumbly, then stir in the oil.
Stir in the water until the mixture forms a dough. It will be very wet but should hold together.
Wrap well and chill the dough for at least 1 hour (and up to 2 days).
When ready to bake, preheat the oven to 400°F (200°C) and line 2 baking sheets with parchment paper.
Working with a quarter of the dough at a time, on a floured surface, roll out to ⅛-inch-thick (3 mm) or less (as thin as possible) and use a 1½-inch (4-cm) round cutter to cut as many circles as you can.
Transfer the circles to a lined baking sheet, then poke holes all over the dough with a toothpick. Brush with the egg wash and sprinkle with some salt.
Bake for 10 minutes, until the crackers are bubbled up and golden brown. I like to bake one sheet at a time.
Melt the remaining tablespoon of butter and brush on the crackers while still warm. Let cool completely on a wire rack while rolling and baking the remaining crackers.
Store in an airtight container at room temperature for up to 1 week.
