To clean sardines, rub off scales with knife and remove heads. Slice open along backbone; pull backbones out of fillets. (This will yield small butterflies of fresh sardine meat.)
Heat 1/2 cup olive oil in large heavy skillet over medium heat. Add onions; stir to coat with oil. Reduce heat to medium-low; cover. Cook, stirring occasionally, until onions are soft and just begin to color, about 30 minutes.
Remove cover. Season with salt and pepper. Make sure there is still enough oil in pan and increase heat to medium. Cook, uncovered, stirring frequently, until onions are deep golden and caramelized, about 25 minutes.
Add garlic and chorizo to onions. Increase heat to high. Stir in wine. Cook, stirring constantly, until wine is reduced but mixture is still moist, about 3 minutes. Stir in olives and parsley.
Slice potatoes into long strings on Japanese turning slicer. Soak potato strings in water for 10 minutes. Drain.
"Blanch" potato in fryer until sticky and soft, about 3 minutes. Do not fry until crisp.
Fill a fillet with 1 to 2 tablespoons caramelized onion/chorizo mixture. Working from head to tail, carefully wrap potato string around fish, adding more strings as needed. (Potato should be 1 layer. Each time potato wraps around sardine, it should be next to potato string above, but not overlapping. When fish is entirely wrapped, no spaces between potato string should be visible.) Repeat with remaining sardines.
Sauté potato-wrapped sardines in olive oil on each side until crisp, 2 to 4 minutes.
Serving suggestion: Plate 3 sardines per portion on bed of pickled carrot; drizzle with salsa verde.