Combine the first three ingredients in a small bowl to make the seasoning mix.
Melt 2 tablespoons of the butter in a heavy 12-inch skillet over high heat. Add the onions and cook, shaking the skillet or stirring occasionally, until they are clear and turning brown on the edges, about 3 minutes. Stir in the bell peppers and cook, continuing to stir or shake the pan, until the onions are soft but the bell peppers are still crispy, about 3 minutes more. Reduce the heat if necessary to avoid burning the vegetables. Transfer the vegetables to a plate to stop the cooking process. Set the skillet aside without wiping it, to use later for saut‚ing the meat.
Heat several sizzle platters or a large cast iron skillet in a 400º oven.
Meanwhile, place the meat strips in a large bowl and sprinkle them with 2 teaspoons of the seasoning mix, tossing to coat well. Pour the lime juice over the meat and toss again. Let marinate at least 10 minutes, tossing occasionally. (After 15 minutes the meat strips will break apart when pulled.)
Heat the unwiped skillet over high heat for 40 to 45 seconds and add the remaining butter (it will sizzle). Pick up the meat with your fingers, let it drain slightly, and add it to the skillet, reserving the marinade. Cook the meat about 45 seconds, turning frequently to coat with butter. Add the reserved vegetables to the meat, and cook for 15 seconds, tossing constantly to combine. Add the reserved marinade, then sprinkle the remaining seasoning mix over all, and cook for 1 minute, still tossing or stirring. Remove from the heat and pour onto heated sizzle platters or cast iron skillet. Serve while still sizzling.
Let everyone prepare his/her own fajitas by using the traditional condiments. The classic method is to lay some meat and cooked vegetables down the center of a tortilla, then sprinkle on the desired condiments and fold one end up, then fold one side in and roll up the remaining side to prevent the goodies from squirting out the end of the tortilla.
Note: Recipe calls for boneless sirloin strip steaks, but you can use skirt steak or London broil -- just be sure to use a cut that's tender enough to broil. Skirt steak is usually about ¼ inch thick, which is perfect; London broil is about ½ inch thick, so you'll need to slice it in half before cutting it into strips.