Place 3 oven trays lined with baking paper in oven and preheat to 200˚C fan-forced. Meanwhile, thinly slice sweet potato and eggplant lengthways into 5mm-thick slices. Divide sweet potato among trays, drizzle with oil and season; bake until tender (12 minutes).
Meanwhile, cook silverbeet in large saucepan of boiling water until tender (3 minutes); drain and refresh. Squeeze out excess water and pat dry on paper towel.
Transfer sweet potato to a bowl. Place eggplant on trays, drizzle with oil and season; bake until tender (15 minutes). Reduce oven to 180˚C fan-forced.
Meanwhile, stir oil and flour in a saucepan over medium heat until bubbling. Gradually whisk in milk; cook, whisking continuously until béchamel boils and thickens (8 minutes). Remove from heat; whisk in nutmeg, three-quarters of the parmesan and egg yolks. Season to taste.
Grease a 20cm x 28cm ovenproof dish. Pour half sugo into dish, then layer sweet potato, silverbeet, remaining sugo, feta and eggplant. Pour over béchamel, scatter with remaining parmesan and paprika; cook until golden (40 minutes). Stand 20 minutes before serving.