What Is Up With Plovers' Eggs

As you know, Megan Abbott and I read a lot of celebrity biographies together. We just read one about Gloria Swanson, in which we learn that "she developed a taste for plovers' eggs." Then we moved on to Clare Boothe Luce: "Mr. Higganbotham gave her an extravagant eleventh 'birthday' feast of plovers' eggs, consommé, turbot, chicken, asparagus, vanilla soufflé, and a cake with eleven candles." Anyway, what the hell is up with plovers' eggs.