Preheat your oven to 220C fan.
Arrange the eggplant and capsicum on a large baking tray. Drizzle with 2 tablespoons of the olive oil and season lightly with salt.
Roast for 40 - 50 minutes, or until the eggplant is completely collapsed and soft and the capsicum is blistered and lightly charred. Remove from the oven and allow to cool slightly.
Meanwhile, bring a large frying pan to low heat with the remaining olive oil. Add the onions along with a generous pinch of salt and cook for 20 - 30 minutes, stirring occasionally, until deeply golden, soft and jammy.
Add the garlic, tomato paste, cumin, coriander and chilli flakes. Cook for a further 3 - 5 minutes, stirring regularly, until the tomato paste darkens and becomes fragrant.
Roughly chop the roasted capsicum then transfer the roasted eggplant to a chopping board and roughly chop it, including all of the skin. You want visible pieces of eggplant skin throughout the filling rather than a smooth purée.
Add the eggplant and capsicum to the onion mixture and stir everything together. Cook for another 2 - 3 minutes until combined.
Taste and adjust seasoning. Add more salt if needed. The filling should be rich, glossy and almost spreadable. If it looks dry, stir through an extra drizzle of olive oil.
Reduce the oven to 190C fan.
Brush a 24 - 26 cm round baking dish with a little melted butter.
Lay one sheet of filo into the dish, allowing it to overhang the edges. Brush lightly with butter. Repeat with another 6 sheets, rotating them slightly each time so they fan out around the dish. Brush each layer with butter.
Spread the eggplant filling evenly into the dish.
Fold the overhanging filo over the filling towards the centre.
Scrunch the remaining 3 sheets of filo over the top and brush generously with the remaining butter.
Bake for 40 - 50 minutes, or until deeply golden and crisp.
Allow the börek to rest for 15 - 20 minutes before slicing into wedges and serving.