Prepare the chicken: Pat dry the chicken thighs with paper towels. Season with salt and pepper.
Sear the chicken: Heat the butter in a large skillet or braiser over medium high/ high heat. Add the chicken, skin side down, and let it sear until it releases from the pan. Flip and sear the other side. Don't worry about cooking it all the way through - it has lots of time to stew. Remove the chicken from the pan. You might have to do this in batches, so repeat with remaining chicken. Transfer chicken to a plate.
Cook the veggies: Reduce the heat and add the mushrooms and onions to the skillet. Saute for about 5 minutes, then add the flour. Cook for another minute and stir well. After that, add the wine and let it cook down for a few minutes, then pour in the broth, lemon juice, sugar and stir.
Cook the stew: Add the chicken pieces back to the skillet in a single layer. Pour in the juices that have accumulated on the plate too.Cover and simmer for 25-30 minutes until the chicken is cooked through. Taste and adjust seasoning as needed.
Finish the fricassee: When the stew is done cooking, adjust for seasoning. To make the sauce thicker, whisk the egg yolks with the cream and temper them by very slowly adding a 1/2 cup of the sauce. Whisk well to avoid scrambling. Stir the egg mixture and remaining 2 tbsp of butter into the fricassee. Garnish with parsley and serve!