In a large saucepan, heat the oil and butter together.
Add the onions, salt and sage and cook for 10 minutes until the onions are starting to soften.
Turn the heat down to its lowest heat, and cook for 30 minutes, stirring occasionally.
Remove the pastry from the freezer and put on the counter to defrost.
Add the balsamic vinegar and sugar to the onions. Stir well and cook for 10 more minutes.
Slide your pastry onto a baking sheet, lined with cooking paper.
Pre-heat your oven 220°C/430°F.
Using a butter knife cut a border inside the tart. You don't want to cut all the way through just score it so that you have guide for the filling and also this helps a little wall rise up around the onion mixture.
Using a sharp knife prick the surface of the inner rectangle to minimise its puffyness.
Spread the onion mixture over the inside of the tart. (You may have too much onion - But it will keep for a few days in the fridge)
Sprinkle over the crumbled feta cheese.
Use a pastry brush the edges of the tart with egg wash and bake for 20 minutes until crispy and golden.