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Heat a grill to high (450u00b0 to 550u00b0). Cut parallel slashes on nopales about 1 in. apart from tips to 1 1/2 in. from bases (keep bases intact). In a small bowl, whisk oil, lime juice, oregano, 3/4 tsp. salt, and the cayenne. Spoon 2 tbsp. dressing into a medium bowl, add steak, and toss to coat; set aside. Brush nopales with a little dressing. Set remaining dressing aside.
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Put lettuce, cilantro, and most of radishes in a large bowl; cover and chill.
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Grill chile, turning often, until blackened all over, about 10 minutes. Grill nopales, turning once, until juices cook off and bright color fades, 6 to 8 minutes.
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Let vegetables cool briefly, then cut nopales into 1/2- by 2-in. strips. Peel, stem, seed, and chop chile. Toss vegetables in a medium bowl with 1/4 cup dressing.
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Grill steak, turning once, until grill marks appear, 4 to 5 minutes. Set on a board; let rest briefly. Slice across grain on a diagonal; toss with nopales and chile.
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Add remaining dressing to lettuce and toss to coat. Arrange on a platter. Put steak mixture in the center. Sprinkle with cotija, pumpkin seeds, and remaining radishes. Season with more salt to taste.
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Nopales Basics:
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BUY. Some supermarkets and Latino markets sell cactus with the spines, and others sell it de-stickered and ready to use--whole or cut up. When buying whole pads, look for ones that are smooth, crisp, and small to medium size.
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PREP. To remove spines from pads, put on dish gloves. Scrape a knife almost flat down the length of both sides of pads to shave off spines and barbed, fuzzy dots. Pare rims with a vegetable peeler. Trim bases; rinse pads.
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COOK. Once nopales hit the heat, they release a sticky juice (like okra), but it cooks off.
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Instructions for sauteing: Cut nopales into 1/2- by 2-in. strips. In a frying pan, saute nopales over high heat with 2 tsp. oil until pan is mostly dry, 5 minutes. Reduce heat; cook until barely tender, 3 minutes more.
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*Find cotija and hulled pumpkin seeds at well-stocked grocery stores and Latino markets. If seeds are raw, saute over medium heat with 1 tsp. oil, stirring often, until golden, 3 to 5 minutes. Salt to taste.
