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Generously season the chicken with salt and pepper.
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Heat one tablespoon of olive oil in a large skillet over medium-high heat.
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Add the chicken and sear on both sides until completely browned and cooked through.
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Remove, put on a plate, and set aside.
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In the same skillet, heat the remaining tablespoon of olive oil.
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Add the onion, garlic, and rosemary to the pan and sauté for 4-5 minutes.
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Add the mushrooms and cook for another 5 minutes until browned.
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Pour in the chicken broth and coconut milk and stir to combine, scraping any browned pieces off the bottom of the pan.
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Bring to a boil, then reduce the heat and simmer for 4-5 minutes until the sauce thickens.
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Add salt and pepper to taste.
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If desired, purée the sauce in a blender until smooth.
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Serve warm sauce drizzled over the seared chicken.