Cook the bacon in a large skillet over medium heat, stirring occasionally, until crisp and evenly browned (about 10 minutes or so). Pour off the fat and drain the bacon on a paper towel-lined plate.
Melt the butter in a saucepan over medium-low heat. Add the flour and stir until the mixture thickens and becomes light golden-brown (about five minutes). Gradually whisk the chicken broth into the flour mixture and bring to a simmer over medium heat. Cook and stir until the mixture is thick and smooth (about 10 minutes). Reduce the heat to low.
Beat the egg yolks and the heavy cream together until blended. Slowly whisk 1/4 of the hot soup mixture into the cream mixture and then return the entire mixture to the soup pot. Whisk in the mustard, then stir in the apple and bacon. Serve immediately.