Preheat the oven to 350 degrees Fahrenheit.
In an a Kitchen Aid mixer fitted with the paddle attachment, cream together the butter and sugar until they are just combined and then add the vanilla extract. Separately, sift together the flour and salt. With the mixer on low speed, add the flour mixture to the creamed butter and sugar. Mix until the dough starts to come together. If the dough looks downy rather than sticky, it's because the butter wasn't quite room temperature-y enough. Fear not. Add a wee bit of hot water until the dough comes together. Then, dump on a floured board and roll together into a flat disk (this will also warm up the butter and soften the dough causing it to come together better). Wrap dough disc in plastic and chill for 30 minutes.
Roll all the dough into 1 1/4-inch balls first. Then, dip each ball into the egg wash and then roll it in coconut. Place the balls on an ungreased cookie sheet and press a deep indentation into the top of each with your fingers. Generously fill each indentation with jam of your choice. Bake for 20 to 25 minutes, until the coconut is a golden brown. Cool and serve.