Shred the sweet potato and onion and place in a medium bowl. Add scallions, flour, baking powder, beaten eggs, cayenne pepper, salt and black pepper. Mix well to combine.
Heat oil in a large cast-iron or nonstick skillet over medium heat. Using a medium cookie scoop, spoon some of the latke batter into the skillet, pressing down lightly to flatten.
Fry until golden brown, about two to three minutes per side, turning just once. Remove and drain on a cooling rack set over paper towels to catch any excess oil.
Preheat oven to 350°F.
In a large skillet over medium heat, sauté diced onions in oil, until lightly golden. Add cubed eggplant and zucchini and continue to cook until vegetables are soft. Stir occasionally to keep vegetables from burning.
Remove from flame and let cool. Add eggs, breadcrumbs, yogurt, and parsley. Season to taste with salt and pepper. Pour mixture into deep round quiche dish and bake for 30 minutes.
Put slices of smoked cheese on top of baked quiche. Top with the sweet potato latkes and bake for an additional 10 minutes to melt the cheese and crisp the latkes.