Remove 1/2 teaspoon zest and squeeze 1 tablespoon juice from lime. In a bowl combine lime zest, lime juice, and the next five ingredients (through chili powder); mix well.
In a bowl whisk together eggs, milk, and salt. In a large skillet melt butter over medium heat; pour in egg mixture. Cook over medium heat, without stirring, until mixture begins to set on bottom and around edges. With a spatula or large spoon, lift and fold the partially cooked egg mixture so the uncooked portion flows underneath. Continue cooking over medium heat 2 to 3 minutes or until egg mixture is cooked through but is still glossy and moist. Immediately remove from heat; fold in cheese.