Make the tempura: Beat eggs in a large bowl until frothy. Stir in 3/4 cup plus 3 tablespoons ice water, 3/4 cup plus 1 tablespoon flour, and salt until just incorporated; batter should still be very lumpy.

Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C). Set a wire rack over several layers of paper towels.

Dry sweet potato slices with paper towels. Dip three slices into batter, letting excess batter drip back into the bowl. Fry in the preheated oil until golden brown, about 2 minutes per side. Use a slotted spoon to transfer sweet potatoes to the wire rack. Repeat to dip and fry remaining sweet potatoes.

Make the dipping sauce: Whisk rice wine and soy sauce together in a small bowl. Serve with tempura.