1. Heat a grill to high (450° to 550°). 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.
2. Put lettuce, cilantro, and most of radishes in a large bowl; cover and chill.
3. 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.
4. 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.
5. 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.
6. 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.
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.
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.
COOK. Once nopales hit the heat, they release a sticky juice (like okra), but it cooks off.
Instructions for sautéing: Cut nopales into 1/2- by 2-in. strips. In a frying pan, sauté nopales over high heat with 2 tsp. oil until pan is mostly dry, 5 minutes. Reduce heat; cook until barely tender, 3 minutes more.
*Find cotija and hulled pumpkin seeds at well-stocked grocery stores and Latino markets. If seeds are raw, sauté over medium heat with 1 tsp. oil, stirring often, until golden, 3 to 5 minutes. Salt to taste.