1. Combine stock ingredients in a 4-quart stockpot and bring to a boil over medium-high heat. Reduce heat and simmer 15 minutes. Reduce heat to the lowest setting to keep stock hot but not evaporating.

2. In another 4-quart pot, heat olive oil over medium-high heat. Cook onion until translucent, stirring, about 2 minutes. Add rice and cook, stirring, until just starting to turn translucent (rice will start making a clicking sound), 1 to 2 minutes. Reduce heat if onion begins to brown.

3. Pour in wine and cook, stirring, just until absorbed (rice should be wet and glistening, not dry). Using a ladle, add 1/2 cup hot stock to the rice. Stir constantly with a wooden spoon, at a moderate speed, until about 3/4 of the liquid is absorbed (the mixture should be thick enough to hold a trail behind the spoon). Continue adding stock, 1/2 cup at a time, and stirring frequently until rice is almost translucent (the rice should be al dente but not crunchy, and liquid is creamy in consistency). As rice nears doneness, watch carefully and add smaller amounts of liquid to make sure it doesn't overcook (you may not need to use all the broth). The process should take 20 to 25 minutes total.

4. Stir in butter until completely melted (this is called mounting), then stir in cheese and season with salt and pepper. Garnish with parsley and drizzle with oil, if desired; serve immediately.