1. Preheat a grill to high heat. Heat the sugar, sherry vinegar, and 2 tablespoons water in the microwave until warm, about 1 minute. Add the shallots and chile to the vinegar and set aside for at least 10 minutes.
2. Toss the squid with 2 tablespoons olive oil, salt, and pepper in a medium bowl. If using an outdoor grill, place the squid in a grill basket and press together to flatten. Alternatively, for indoor grill pans, weigh the squid bodies down with a cast-iron skillet or bacon press. Grill on both sides until cooked through, about 2 minutes per side. Slice the bodies into rings and divide evenly among 4 shallow bowls with the tentacles.
3. Drizzle the remaining 2 tablespoons olive oil over the parsley in a medium bowl and toss with the shallots and vinegar. Season with salt and pepper. Mound the salad on the squid and spoon the vinegar over top. Garnish with a lemon wedge and serve.
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