The halloumi soak is not optional. Twenty minutes in cold water pulls out enough of the brine that you can eat a plateful. Skip it and the cheese runs the dish.
Roast the vegetables in one layer. Heaped on a small tray they steam instead of caramelising, and roasting them separately is the whole reason the aubergine holds its own against the sauce.
Judge the sauce by thickness, not the clock. Ten minutes is a guide. It should hold a line when you draw a spoon through it, or it will slide off the bread.
Watch the grill. Halloumi goes from blistered and golden to dry and squeaky in a couple of minutes, and it does not come back.
There are no eggs in this. The halloumi is standing in for them. If you want both, make wells and poach the eggs in the sauce before the cheese goes on top.