Preheat the oven to 220℃ (200℃ fan)/425°F/gas mark 7. Cut the carrots into thick batons. Cut the onions into thick wedges. Spread out on a baking sheet and drizzle with 2tbsp of the oil.
Place the salt and spices in a pestle and mortar and coarsely grind. If you do not have a pestle and mortar you can crush them between two spoons or on a board with the end of a rolling pin.
Sprinkle most of the seasoned salt over the carrots and onions and toss the vegetables on the tray to coat with the oil and spices. Roast for 25-30 minutes until tender and lightly browned at the edges. Reduce the oven temperature to 200℃ (180℃ fan)/405°F/gas mark 6.
Melt the butter with the remaining oil. Lay a clean tea towel on the work surface and place one sheet of filo on top with the longest end closest to you. Brush with some of the melted butter.
Place another sheet of filo on top and brush with melted butter. Repeat until you have a stack of 4 sheets of filo.
Spoon half of the roasted carrots and onions in a line along the furthest edge of the filo from you. leaving a gap at either end so that you can fold the pastry up over the filling. Squeeze a little lemon juice over the carrots and sprinkle with half of the chopped mint.
Crumble half the feta over the carrots. Fold the ends of the pastry over the filling, then using the tea towel to help you, roll the strudel towards you to enclose the filling.
Carefully transfer to a large baking sheet and brush the top with more melted butter. repeat to make a second strudel then sprinkle the remaining spiced last over the top of both strudels.
Bake for 25 to 30 minutes until crisp and golden brown.
This dish can be prepared up to 1 day in advance. Cover with cling film or foil and store in the refrigerator.Reheats well.Not suitable for freezing.