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Add olive oil to a large skillet and heat for a minute over medium/high heat. Season chicken with salt and pepper and then add to the hot pan. Cook chicken for five minutes, tuning each piece once. After five minutes, remove from pan, place on a plate off to the side.
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Reduce heat to low, add onion. Sauté onion for three minutes. Add the garlic and cook for one minute. Add rice to pan, stir for a minute or two to toast the rice.
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Pour in the chicken stock. Bring to a simmer with the lid on. Simmer rice for fifteen minutes.
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Eight minutes into the rice cooking, add the broccoli to the rice. Cover with lid and continue cooking rice while the broccoli steams.
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Add the salt, pepper, paprika, and crushed red pepper flakes to the broccoli and rice. Stir to combine. Add in the chicken and tarragon, stir to combine. Sprinkle cheese on top of broccoli, chicken, and rice. Cover with lid and let stand for two to three minutes, until the cheese melts. Stir the melted cheese into the dish. Serve right away. Reheat in microwave or in a pan with a little bit of warmed chicken stock. Dish will last four days in the refrigerator in an airtight container.