Using a mandoline, slice the potatoes and onion thinly. If you don't have a mandoline, slice them with a knife instead, though it takes more time. A mandoline speeds things up and keeps every slice the same thickness, so the tart bakes evenly.
Lightly spray a casserole dish with olive oil.
Arrange the white potato slices in the dish in a circular, overlapping pattern, each slice on top of half of the one before it, like when you make an apple pie. Tuck the sweet potato and onion slices in randomly between the white potato slices.
In a separate bowl, whisk the 2 eggs. Stir in the grated feta cheese, salt, pepper and thyme. Pour this mixture evenly over the potatoes in the dish. Using a fork, gently spread it so most of the slices are coated.
Place in a preheated oven at about 180ºC/356ºF and bake for 30-40 minutes. Check for doneness with a fork: if the potatoes are tender, the tart is ready.
Once baked, let it cool slightly. Remove from the dish and sprinkle with smoked paprika and fresh parsley before serving.