Place the skirt steaks in a glass baking dish and season generously with salt and pepper.

In a medium bowl, combine 2 tablespoons of the fresh lime juice with the thinly sliced onion, pressed garlic, hot chili sauce, ground cumin, and finely grated lime peel to create the marinade. Pour the marinade evenly over the steaks and let it sit for 10 minutes.

Heat 2 tablespoons of olive oil in a large nonstick skillet over high heat. Add the steaks along with the onion mixture and sear the steaks for about 1 minute per side.

Add the cherry tomatoes and thinly sliced fresh basil to the skillet, then continue cooking the steaks. Cook for an additional 3 minutes for medium-rare, turning them occasionally.

Sprinkle the remaining 1 tablespoon of lime juice over the pan and cook for one more minute to let the flavors meld.

Transfer the steaks to a cutting board and let them rest for a few minutes. Slice thinly against the grain and serve the meat along with the pan juices on warm tortillas.

For best results, warm your tortillas directly over a gas flame for about 10 seconds per side or heat them in a dry skillet before serving.