Add the eggs, smoked paprika, and salt to a large mixing bowl. Whisk to combine. Fold in the grated sweet potatoes and scallions.
Heat a 12” stainless steel skillet over medium heat. Add 2 tablespoons of olive oil. Once hot (the oil will shimmer), spoon about 2 tablespoons of the sweet potato mixture into the skillet at a time, flattening it down to create a cake. You should be able to fit about 4-5 cakes in the skillet at once.
Cook for about 4 minutes until golden and crisp on one side. Use a metal spatula to flip the cakes and cook for another 4 minutes. Adjust the heat throughout the cooking as needed (medium-low if they’re getting too dark / back to medium when they’re not crisping enough).
Transfer the cakes to a sheet pan lined with paper towels to drain. Immediately sprinkle with flaky sea salt (or kosher). Repeat with the remaining mixture, adding more olive oil to the skillet as needed.
Meanwhile, add the greek yogurt, dill, lemon zest, and lemon juice to a food processor. Process until smooth. Season with salt and pepper to taste.
Serve the sweet potato cakes immediately with the dill yogurt sauce alongside.