Heat olive oil in a skillet over medium-high heat. Add chicken and sear until lightly browned, 2 to 3 minutes per side. Remove from the skillet.

Add drained mushrooms to the juices in the skillet and cook until they start to pop, about 5 minutes.

Whisk together cream, egg yolk, Dijon mustard, salt, and pepper in a small bowl; pour into the skillet with the mushrooms. Return chicken breasts to the skillet and simmer over medium-low heat, stirring occasionally to prevent the egg yolk from setting, until chicken is no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center of the chicken breast should read at least 165 degrees F (74 degrees C).

Serve with cooked white rice.