Prepare the Brown Butter: In a cast iron skillet, melt the butter over medium heat. Allow it to brown for approximately five minutes, until it achieves a darker color and a nutty aroma.
Cook the Lobster: Season the split lobster tails with salt and white pepper. Place the lobster, cut-side down, into the brown butter. Cook for four minutes, then flip the lobster to the shell side and continue cooking until the shell turns bright red (about one minute).
Make the Corn Salad: In a bowl, combine the corn, cilantro, and green onions. Season with lime juice, salt, and pepper, then toss gently to combine.
Serve: Arrange the corn salad over the cooked lobster.