This trial tests if a special low-carb diet or a ketone drink can help people with type 1 diabetes manage low blood sugar and improve brain function. The diet makes the body produce ketones, which the brain can use for energy when blood sugar is low. Researchers will compare brain activity during low blood sugar episodes in participants following the diet versus those who are not. The low-carbohydrate, ketogenic diet (LCKD) has been studied for its potential to improve blood sugar management and reduce medication use in diabetes care.