Start by seasoning the steak with salt and pepper on both sides. In a small bowl, mix together the lime juice, minced garlic, and chopped rosemary. Rub this mixture onto the steak, cover, and let it marinate in the fridge for at least 30 minutes.
Heat a cast-iron skillet or grill pan over medium-high heat. Drizzle with olive oil to prevent sticking and enhance browning.
Once the pan is heated, carefully place the steak in the skillet. Sear for about 4-5 minutes per side, depending on your desired level of doneness.
In a small pot, melt the butter over low heat. Add the remaining minced garlic and simmer for a few minutes until fragrant. Stir in a pinch of salt and any leftover marinade.
During the last minute of cooking, pour the garlic butter over the steak and let it baste for added richness. After cooking, let the steak rest for about 5-10 minutes before slicing.
Using a sharp knife, slice the steak against the grain into strips. Arrange on a platter and drizzle more garlic butter sauce over the top before serving.