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1
Pat chicken dry with paper towels and season with 1 teaspoon salt and 1/2 teaspoon pepper.
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2
Heat butter and oil in 12-inch skillet over medium-high heat.
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3
When foaming subsides, place chicken in skillet and cook until browned, about 4 minutes.
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4
Flip chicken and continue to cook until browned on second side, about 4 minutes longer.
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5
Transfer chicken to large plate.
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6
Add mushrooms, onion, and wine to now-empty skillet and cook, stirring occasionally, until liquid has evaporated and mushrooms are browned, 8 to 10 minutes.
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7
Add flour and garlic; cook, stirring constantly, 1 minute.
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8
Add broth and bring mixture to boil, scraping bottom of pan with wooden spoon to loosen browned bits.
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9
Add chicken and any accumulated juices to skillet.
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10
Reduce heat to medium-low, cover, and simmer until instant-read thermometer registers 160 degrees when inserted in breasts and 175 degrees when inserted in thighs, 5 to 10 minutes.
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11
Transfer chicken to clean platter and tent loosely with foil.
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12
Whisk sour cream and egg yolk together in medium bowl.
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13
Whisking constantly, slowly stir 1/2 cup sauce into sour cream mixture.
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14
Stirring constantly, slowly pour sour cream mixture into simmering sauce.
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15
Stir in nutmeg, lemon juice, and tarragon; return to simmer.
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16
Season to taste with salt and pepper.
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17
Pour sauce over chicken and serve.
