Cook the bacon in a large, deep skillet over medium heat, stirring occasionally, until crisp and evenly browned, about 10 minutes. 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 becomes paste-like and light golden brown, about 5 minutes. Gradually whisk the chicken stock into the flour mixture and bring to a simmer over medium heat. Cook and stir until the mixture is thick and smooth, 10 to 15 minutes. Reduce heat to low.
Beat the egg yolks and heavy cream together until blended. Slowly whisk 1/4 of the hot soup into the cream mixture and return the cream mixture to the soup pot. Whisk in the mustard; stir in the apple and bacon. Cook and stir until the soup is hot but not simmering.