For risotto:

• 6 cups chicken stock
• 2 cups hot water
• 3/4 stick unsalted butter, divided
• 1 medium onion, finely chopped (1 cup)
• 3 garlic cloves, finely chopped
• 1 pound Arborio rice (2 1/2 cups)
• 2/3 cup dry white wine
• 1/2 cup grated Pecorino Romano

For radishes:

• 1 tablespoon white-wine vinegar
• 1 tablespoon extra-virgin olive oil
• 1 bunch trimmed radishes, julienned
• 1 tablespoon finely chopped chives

Make risotto:
Bring stock and water to a simmer in a 3-to 4-quart saucepan. Meanwhile, heat 3 tablespoons butter in a 4-to 5-quart heavy pot over medium heat until foam subsides, then cook onion, stirring occasionally, until just softened, about 5 minutes. Add garlic and cook, stirring occasionally, until softened, 6 to 8 minutes. Stir in rice and cook, stirring, 1 minute. Add wine and cook, stirring, until absorbed, about 1 minute.

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. Thin with some of remaining broth if necessary (you will have some left over). Remove from heat. Stir in cheese, 1 teaspoon salt, 1/2 teaspoon pepper, and remaining 3 tablespoon butter.

Prepare radishes:
Whisk together vinegar, oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Toss radishes with dressing and chives. Serve risotto topped with radishes.