Heat the mushroom soaking liquid with the chicken broth in a 3-quart saucepan over medium heat. Meanwhile, in a large (4-quart) pot, melt 2 Tbs. butter over medium-high heat. Add the onion and sprinkle with 1/2 tsp. salt. Cook the onion, stirring, until it softens and turns a light brown, about 3 minutes. Add the rice and mushrooms and cook, stirring, for 1 minute.
Add the sherry; raise the heat to high, and cook, stirring, until it almost completely reduces, about 1 minute.
Reduce the heat to medium; add 3/4 cup of the broth to the rice, and cook, stirring often, until the rice absorbs the broth, 2 to 3 minutes. Add another 3/4 cup of broth and cook until absorbed. Continue adding broth in this manner until the rice is creamy and tender, about 20 minutes total—you may or may not need all of the broth. Stir in the arugula, Parmigiano, all but a couple tablespoons of the chives, and the remaining 2 Tbs. butter and continue stirring until the arugula is just wilted, about 1 minute. Serve immediately in individual bowls, sprinkled with a few grinds of black pepper and the remaining chives.