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Step 1
Pat 3 pounds bone-in chicken thighs or drumsticks with paper towels. Season with 1 teaspoon of the kosher salt and 1/2 teaspoon of the black pepper and let sit for 5 minutes.
Step 2
Melt 3 tablespoons unsalted butter in a large Dutch oven or heavy-bottomed pot on medium heat. Add half of the chicken skin-side down and sear until the bottom is dark golden-brown, 12 to 15 minutes. Transfer to a large plate skin-side up (it will not be cooked through). Repeat searing the remaining chicken and adding to the plate.
Step 3
Add 1 sliced large white onion and 8 to 10 ounces quartered cremini mushrooms to the pot. Season with the remaining 3/4 teaspoon kosher salt and 1/4 teaspoon black pepper. Cook, stirring occasionally and scraping up any browned bits from the bottom, until the onion is softened, 3 to 5 minutes.
Step 4
Sprinkle 3 tablespoons all-purpose flour over the mushrooms and onions and toss until evenly coated. Stir in 3/4 cup dry white wine and cook until reduced by half, about 5 minutes. Stir in 1 1/4 cups warm water, 2 fresh parsley sprigs, 2 fresh thyme sprigs, and 1 dried bay leaf. Return the chicken and any accumulated juices to the pot, arranging the chicken skin-side up. Bring to a boil.
Step 5
Reduce the heat to maintain a simmer. Cook uncovered, stirring occasionally, until the sauce is reduced slightly and deeply flavored, and the chicken is very tender, about 50 minutes.
Step 6
Stir in 3/4 cup heavy cream and cook gently on medium-low heat for 5 minutes for the flavors to meld. Remove the pot from the heat and let cool for 10 minutes.
Step 7
Place 2 large egg yolks in a small bowl. While whisking with a fork, slowly pour in about 1/4 cup of the cooking liquid and whisk until combined. Stir the egg mixture into the chicken fricassée until combined. Remove and discard the herbs stems and bay leaf. Taste and season with more kosher salt and black pepper as needed. Garnish with chopped fresh parsley leaves and serve with potatoes, bread, or pasta.