Step 1Bring the chicken stock and 4 cups water to a boil in a large saucepan. Add any assorted herb stems and trimmings and then reduce the heat to maintain a lazy simmer.
Step 2In a large skillet or pot over medium-low heat, cook the minced green onion and arugula in 2 tablespoons butter until the onion is soft and fragrant, about 5 minutes.
Step 3Add the rice and increase the heat to medium. Cook, stirring, until the rice makes a kind of clicking or "singing" sound as it scrapes the bottom of the pan and you can see the outside of the kernel become translucent, about 2 to 3 minutes. Add the wine and cook, stirring, until it evaporates completely, about 3 minutes.
Step 4Begin adding the simmering stock, straining out the trimmings, between three-quarters and 1 cup at a time. Cook after each addition until the stock has evaporated enough so that you can see the bottom of the pan come clean when you scrape it with a wooden spoon, about 5 minutes. Add the salt.
Step 5Repeat, adding more stock each time, until the rice is chewy but tender, with no chalky center. This will take about 20 minutes in all. You don't need to stir continuously, just when you add the stock to the pan and when it is nearly dry. You will not use all the stock. At the last addition, add the chopped arugula and the minced tarragon.
Step 6When the rice is done, add another half-cup of stock to loosen the mixture slightly. Remove the pan from the heat. Add the Parmigiano-Reggiano and the remaining 2 tablespoons butter and beat it into the rice.
Step 7Spoon the risotto in generous mounds in the centers of heated flat bowls. Serve immediately.