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Wash the chicken breasts and pat them dry with a paper towel.
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Season the chicken on both sides with kosher salt and freshly ground black pepper and set aside.
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Drain the apricots, reserving 1/3 cup of the nectar. Discard the rest or keep for future use.
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Place the apricots in a blender or food processor and puree.
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Heat the butter in a large skillet. Add one tablespoon of the thyme leaves and saute.
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Add the chicken breasts to the skillet and cook on both sides.
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Transfer the chicken breasts to a plate, cover with aluminum foil and stow in a warm place.
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Add the minced garlic to the pan and stir until it releases its aroma.
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Add the onions and cook, stirring frequently until they become transparent.
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Add the white wine to the pan and deglaze.
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Stir in the chicken broth and heavy cream and bring to a boil.
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Add the apricot puree to the pan and stir to combine. Let cook for 5 minutes.
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Season with salt, pepper, apricot nectar, and sugar and to taste.
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Reduce the heat and let simmer for 15 minutes.
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Stir in the remaining two tablespoons of thyme leaves.
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Add the chicken breasts, stir to coat and let the mixture simmer for another 5 minutes.
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Remove from heat, transfer to a serving platter, garnish with fresh thyme sprigs and serve.