In a medium bowl, whisk together the lime juice, 1 tablespoon of the olive oil, cumin, chili powder, garlic powder, salt, smoked paprika, and cayenne if using. Add the chicken strips and toss until every piece is coated. Let the chicken marinate for at least 10 minutes at room temperature, or up to 8 hours in the refrigerator if you are planning ahead.

Set a 12-inch cast iron skillet over high heat and let it get very hot, about 2 to 3 minutes. The pan should feel intensely hot when you hold your hand a few inches above it. Add about 1 teaspoon of oil and swirl it to coat the bottom.

Lift the chicken strips out of the marinade with tongs, letting any excess drip off, and lay them in the skillet in a single layer. Do not crowd the pan. If needed, cook in two batches. Let the chicken sit undisturbed for 2 to 3 minutes so it gets real color on the bottom. Flip and cook another 2 to 3 minutes until cooked through and the edges have some char. Remove the chicken to a plate.

Add the remaining tablespoon of olive oil to the skillet. Add the sliced peppers and onion in a single layer. Again, resist the urge to stir constantly. Let them sit for 2 to 3 minutes so they pick up some color on the bottom, then toss and cook for another 3 to 4 minutes until the onions are soft and the peppers have charred edges. Season with a pinch of salt.

Return the cooked chicken to the skillet with the peppers and onion and toss everything together. Cook for 1 more minute so the flavors come together and the chicken heats through. Taste and adjust seasoning with salt or a squeeze of lime juice.

Serve the fajita filling straight from the skillet with warm flour tortillas, sour cream, salsa, and lime wedges on the side. Set the skillet on a trivet at the table and let everyone build their own. The filling holds well in the pan over the lowest heat setting for about 10 minutes if dinner is not quite ready.