1. Light the grill. In a medium bowl, toss the squid with 1/4 cup of the oil and 3/4 teaspoon of the salt.
2. In a large glass or stainless-steel bowl, combine the lemon juice, vinegar, the remaining 1/4 teaspoon salt, and the pepper. Stir in the remaining 1/2 cup oil with a fork. Stir in the basil.
3. Grill the squid quickly over high heat, turning once, until just done, 1 to 2 minutes per side. Remove. When cool enough to handle, cut the bodies into 1/2-inch rings and cut the tentacles in half. Add the squid, lettuce, pimientos, olives, and scallions to the dressing and toss.
Variation: Shrimp can replace the squid. Toss a pound and a half of large shelled shrimp with the oil and salt, as in Step 1, and grill or broil them until just done, turning once, about five minutes in all.
Wine Recommendation: A light, high-acid wine is a must to stand up to the lemon and vinegar in the dressing here. To highlight the squid, serve a vibrant, fruity pinot grigio from the Alto Adige.