Before Eric Adams can start explaining the conspiracy that took him down, the soon-to-be-former mayor of New York City must make his morning smoothie. On a chilly recent Friday, he is standing in the stainless-steel kitchen of Gracie Mansion, the stately official residence on the Upper East Side, layering blueberries and ginger and flaxseed and greens into a Nutribullet blender.“People think that our stomachs are like a washing machine—that when you eat, everything mixes up together—and it is not,” he says, whirring the mixture into a greenish-brown sludge. “Our stomachs are like a sink, where what you put in it...