Peel the sweet potatoes and grate them using the large holes of a box grater or a food processor with a grating attachment. Place the grated sweet potatoes in a clean kitchen towel or several layers of paper towels. Squeeze firmly over the sink to remove as much moisture as possible—this is key for crispiness.
In a large bowl, combine the squeezed sweet potatoes, grated onion, beaten eggs, cornstarch, garlic powder, smoked paprika, black pepper, and 1 tsp salt. Mix thoroughly until everything is evenly distributed and the mixture holds together when pressed.
While the hash brown mixture rests, prepare the sauce. In a small bowl, combine the Greek yogurt (or vegan sour cream), chopped chives, parsley, dill, minced garlic, lemon juice, salt, and pepper. Stir well, taste, and adjust seasoning if needed. Cover and refrigerate until ready to serve.
Heat 2 tbsp of oil in a large skillet over medium-high heat. Scoop about 1/3 cup of the sweet potato mixture per hash brown, form into a compact patty about 1/2-inch thick, and gently place in the hot oil. Fry 3-4 patties at a time, without crowding the pan, for 4-5 minutes per side until deeply golden brown and crispy. Transfer to a paper towel-lined plate.
Stack 2-3 hash browns per plate. Garnish with additional chopped chives and parsley. Serve immediately with the herb dipping sauce on the side.