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Preheat oven to 350 F.
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In a large skillet, heat 1 tsp oil over medium heat. Stir in onion and cook until it begins to soften, about 5 minutes. Add the beef and cook over medium-high heat, stirring occasionally to break up the meat, until no longer pink, about 5 minutes. Pour off any standing liquid. Stir in the chili powder, cumin, ½ tsp salt and pepper. Cook, stirring often for 1 minute. Remove from heat and stir in green chilies.
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In medium skillet, heat 2 tbsp oil over medium-high heat until it is hot but not smoking. Line a plate with paper towels. Fry a tortilla for about 10 seconds on each side, using tongs to flip it. Transfer to the paper towels and very lightly season with salt. Continue with remaining tortillas, stacking them between paper towels. Add more oil to skillet if needed.
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Spread ¼ cup enchilada sauce into the bottom of a 9x13 baking pan. Pour about ½ cup of enchilada sauce onto a plate.
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Working one tortilla at a time, place it in the sauce on the plate to coat the bottom. Spread ⅓ cup of the meat mixture down the center, sprinkle a little cheese, and roll up the tortilla. Place it seam side down in the baking dish. Repeat to form a total of 8 rolls, nestling them against one another in the dish. Pour the remaining sauce over the rolls, and then sprinkle the remaining cheese on top.
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Bake until browned on top and gently bubbling around the edges, about 30 minutes. Let stand for 10 minutes.
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Serve warm with green onions and sour cream.