Preheat the oven to 400°. Set a large rack over a large rimmed baking sheet. In a small bowl, combine the five-spice powder with 1 teaspoon of salt.

In a large saucepan, heat 1 inch of vegetable oil to 350°. In a shallow bowl, beat the eggs. Spread cornstarch in another shallow bowl. Working in four batches, dip the squid in the egg; squeeze out any excess egg. Dredge the squid in the cornstarch, shaking off any excess. Add the squid to the hot oil and fry until golden and crisp, about 1 minute. Using a slotted spoon, transfer the squid to the rack. Season lightly with salt and pepper. Repeat with the remaining squid.

In a large skillet, heat the olive oil. Add the scallions, garlic, onion and jalapeño and stir-fry over high heat until fragrant, 2 minutes. Add the squid and stir-fry until just heated through. Sprinkle with the five-spice mixture. Transfer to a platter or shallow bowl and serve right away with lime wedges.