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1
Place ancho chiles, chiles de arbol, pasilla chile, and aji amarillo chile in a large heatproof measuring glass and pour boiling water over to submerge. Cover with plastic wrap and let sit until chiles are softened, 20-25 minutes. Drain.
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2
Remove seeds from chiles; discard. Remove tops from radishes and coarsely chop. Thinly slice radishes and set aside for the salad. Combine chiles, radish tops, garlic, vinegar, lemon juice, honey, and paprika in a blender; season with salt and pepper. Blend until chiles are finely chopped. With the motor running, stream in oil; blend until dressing is emulsified and smooth.
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3
Prepare a grill for high heat. Cover the underside of a large cast-iron skillet with 2 layers of foil and set on grate (you want it to have time to get very hot).
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4
Working one at a time, butterfly squid bodies. Cut a slit from wide opening to pointed end of body and open up into a flat triangle. Remove the thin clear sliver of cartilage; discard. Using the back of your knife, scrape away the jellylike membrane lining the inside of the body. Rinse bodies and tentacles well; pat dry with paper towels.
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5
Combine garlic, mayonnaise, vinegar, several pinches of salt, and a few cranks of pepper in a large plastic resealable bag. Add squid, seal bag, pressing out air, and massage to coat squid in marinade. Chill 30 minutes.
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6
Lightly oil grate (grate must be clean, so give it a scrub with a wire brush before oiling if needed). Remove squid from bag, letting marinade drip off. Place a few pieces flat on grate and immediately set hot skillet on top (you want to work in a small enough area and with few enough pieces that the skillet covers all the squid at once). Grill until marks appear, about 45 seconds, then uncover squid and turn over (pieces will curl a bit). Set skillet back on top and grill until marks appear on second side, about another 45 seconds. Transfer squid to a medium bowl. Continue with remaining squid.
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7
Add lemon juice to bowl with squid and season with a bit more salt; toss to coat. If bodies are very large, cut into smaller pieces; transfer to a platter. Drizzle several tablespoonfuls of dressing over (reserve the rest for serving with grilled meats or scrambled eggs).
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8
Toss parsley, chives, marjoram, lemon juice, and reserved radishes in a medium bowl; season with salt and pepper. Scatter salad over squid; top with olives and drizzle with oil.
