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Make risotto: Bring broth and water to a simmer in a 3-to 4-quart saucepan.
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Meanwhile, heat 3 tablespoons butter in a 4-to 5-quart heavy pot over medium heat until foam subsides,
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Then cook onion, stirring occasionally, until just softened, about 5 minute
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Add garlic and cook, stirring occasionally, until softened, 6 to 8 minutes.
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Stir in rice and cook, stirring, 1 minute.
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Add wine and cook, stirring, until absorbed, about 1 minute.
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Stir 1 cup simmering broth into rice and cook, stirring constantly and keeping at a strong simmer, until absorbed. Continue cooking and adding broth, about 1 cup at a time, stirring frequently and letting each addition be absorbed before adding next, until rice is just tender and creamy-looking but still al dente, 18 to 22 minutes.
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Thin with some of remaining broth if necessary (you will have some left over). Remove from heat.
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Stir in cheese, 1 teaspoon salt, 1/2 teaspoon pepper, and remaining 3 tbs butter.
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Prepare radishes:
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Whisk together vinegar, oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
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Toss radishes with dressing and chives.
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Serve risotto topped with radishes.