1.  Clean chicken and pat dry with paper towels.  Salt and pepper the chicken.

2.  In a large skillet or dutch oven, heat butter and olive oil over Medium High heat until frothy.  Add chicken and cook until browned on one side, 4 minutes.  Flip the chicken and brown the other side, 4 minutes more.  3.  Remove the chicken from the pan and set aside.

4.  Add 1/4 cup broth to the pan along with onions and mushrooms.  Cook until liquid has evaporated, 8-10 minutes.  Add garlic and cook for 1 minute.

5.  Mix together arrowroot powder and remaining 1 1/2 cup broth and stir well to dissolve.  Add to the pan and bring to a boil.  

6.  Add chicken and any released chicken juices back to the pan.  Reduce heat and cover the pan.  Simmer until chicken reaches 175 degrees F, 5-10 minutes.  Remove chicken from the pan and tent with aluminum foil.

7.  Whisk together egg yolk and sour cream.  Quickly whisk 1/2 cup pan sauce into sour cream mixture.  Return the mixture to the pan and mix well to combine.  

8.  Stir in thyme and lemon juice and return to simmer. Season to taste with salt and pepper. 

9.  Pour sauce over chicken and serve.