Preheat oven to 475°. Line a sheet pan with parchment paper. On parchment, toss potato, onion, 1/2 tbsp. oil, and 1/4 tsp. salt. Set chile and tomato in corner of sheet pan. Bake, turning vegetables once, until browned, about 20 minutes.
In a frying pan, sauté nopales over high heat with 1/2 tbsp. oil and 1/4 tsp. salt until pan is mostly dry, 3 to 6 minutes, then reduce heat and cook until barely tender, 3 to 4 minutes more. Set aside.
Peel, stem, and seed chile; peel tomato. Chop both. In a bowl, whisk eggs with remaining 1/4 tsp. salt and the pepper.
Heat a large skillet over medium-high heat. Add remaining 2 tbsp. oil and the cumin; cook until fragrant, 1 minute. Stir in potato mixture, chile, tomato, and nopales. Cook until hot. Pour in eggs and cook, stirring often, until set, 3 minutes. Sprinkle cheese on top; stir a few times until it melts. Serve with hot sauce.
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.