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Melt coconut oil in a large pan over medium heat. Add onion and carrots and cook until softened. Add dried marjoram, flour, and seasoning packet from the rice; stir to combine.
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Add rice, chicken broth, and water; bring to a boil. Cover, lower to a simmer, and let cook for 15 minutes.
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Heat heavy cream and milk in a small saucepan over low heat. Stir into the soup. Stir in the shredded chicken.
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Cook about 30 minutes or until the rice is cooked. Season with salt and pepper to taste.