The claim: Eating too much broccoli, cauliflower or Brussels sprouts can interfere with thyroid function. The facts: It’s true that these foods, which are described as goitrogenic, can make the thyroid function less efficiently, says Dr. R. Mack Harrell, an endocrinologist with Memorial Health Systems in Hollywood, Fla., because they can prevent the thyroid from getting enough iodine to function properly.