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In a wide pan over medium high heat, sauté the onion and butter until softens, about 5 minutes.
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Add the carrots, salt and pepper. Stir together and continue cooking until vegetables are soft, another 5 to 10 minutes.
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Add garlic and cook until fragrant, about 1 minute.
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Pour the pasta into the pan and stir with the vegetables and toast for 1 minute.
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Add the chicken stock and heavy cream.
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Bring to a simmer, then cover and cook for 12 minutes, stirring occasionally. If the pasta gets too dry, add more stock, water or cream. It should be a loose, creamy consistency.
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While the orzo is simmering, prepare broccoli according to package instructions.
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When the orzo is done, add the broccoli and cheese to the pan and stir together until smooth. Season with more salt and pepper.