Put the flours and the salt in a food processor and pulse to mix. Add the egg, butter and oil and pulse until like small breadcrumbs.
Add the water a tablespoon at a time until the mixture is coming together in larger lumps. Remove from food processor, press together and cover and refrigerate for around 30min.
Meanwhile preheat oven to 400F/200C.
Dice the eggplant and potato into small pieces, approx up to ⅓in/1cm. Dice the onion to a similar size. Spread all on a baking sheet so they are in a single layer, toss with some olive oil and the oregano.
Bake for around 10-15min until the potato is cooked and starting to brown. Remove from oven and set aside to cool slightly.
Roll out the dough on a floured surface until about as thin as you are comfortable with (around ⅛in/2-3mm) and cut out circles - I used my largest scone/pastry cutter which is about 2 ¾in diameter.
Crumble the feta and add to the potato-eggplant mixture then spoon heaped spoonfuls of the mixture into the center of each pastry circle - they should look as if they'll be fairly full.
Carefully pull together the sides of the pastry and use a little water to stick the edges together - this is easiest by bringing together at the middle then working to one side before then working back along the whole edge. If you like, crimp the edge as you go by gently pulling the underneath side over the edge and tucking in.
Lightly oil a baking sheet and bake for approx 20min until the empanadas are starting to brown.