Cookie Monster Veggie Monster, Are known to have a mother, a younger sister, and an identically-designed cousin, who share their distinctive blue skin and “eyes”. He also has a father who appeared in a theatrical sketch Monsterpiece promote energy conservation, water conservation and environmentalism. Both mother and father Cookie Monster that his enormous appetite. He and his Sesame Street friends are popular motifs on t-shirts, and has also guest-starred on the Martha Stewart. Naturally, I was very pleased by the fact that they were making cookies. He also appeared in an episode of 2008.