For the Squid
¼ cup olive oil, plus more for the grill
2 pounds whole squid, cleaned, long tentacles trimmed if desired
For the Green Goddess Dressing
Extra-virgin olive oil, for drizzling
Make the squid: In a large bowl, whisk together the olive oil, wine, garlic, oregano, red pepper flakes, paprika, and salt. Add the squid, toss to coat, then cover and marinate in the refrigerator for 3 to 4 hours.
While the squid marinates, make the Green Goddess
dressing: In a food processor, combine the mayonnaise, buttermilk, chives, parsley, tarragon, lemon juice, anchovy fillets, and garlic. Process until smooth, then transfer to a bowl and season with salt and black pepper. Cover and refrigerate until ready to use; the dressing will keep, refrigerated, for a few days.
Prepare a charcoal or gas grill for direct, high-heat grilling. Lightly oil a perforated grill pan or a cast-iron grill griddle and set it on the grill to preheat.
Remove the squid from the marinade and place on the preheated rack or griddle. Grill for 4 minutes, turning once, or until the squid are almost opaque all the way through and have crisped around the ends and tentacles. Do not overcook, or the squid will become rubbery, but don’t undercook it, either—it should be cooked through, not just charred on the exterior and warm inside.
Smear the dressing onto a large platter and top with the grilled squid. Arrange the pieces of avocado alongside. Drizzle with a ribbon of olive oil, garnish with radishes and a sprinkle of poppy seeds, and season with salt. Serve immediately.