How to Make It
In a medium saucepan, bring the chicken stock and carrot juice to a simmer; keep warm.
In a large saucepan, heat the olive oil. Add the shallot and cook over moderate heat, stirring, until softened, about 4 minutes. Add the rice and cook, stirring, until slightly milky colored, about 1 minute. Add the wine and 2 tablespoons of the vinegar and cook, stirring, until the liquid is absorbed. Stir in the hot stock mixture, 1 cup at a time, stirring constantly and adding more stock once it has been absorbed, about 20 minutes total; the rice should be al dente and suspended in a thick, creamy sauce. Add the cheese and 1 tablespoon of the butter, season with salt and pepper and stir until creamy.
In a medium skillet, melt the remaining 1 tablespoon of butter. Add the peas, season with salt and pepper and cook over moderately high heat until warmed through, about 1 minute. Add the remaining 1/2 tablespoon of vinegar to the peas, then fold into the risotto. Serve immediately.