Make a chive butter: Dip the chives in boiling water for 20 seconds, drain, and put into a food processor. Puree for 1 minute. Add the lemon zest and all but 2 tablespoons of the butter. Process for several minutes, until very smooth and green. Cover and refrigerate.
Put the rice and the remaining 2 tablespoons butter in a large, heavy saucepan over medium heat. Cook, stirring, until all the butter has melted and the grains of rice are translucent, about 6 minutes.
Pour in 1 cup of the wine and cook, still stirring, until the wine has evaporated. Add 1 cup of the stock and continue to cook and stir, adding another 1 cup stock as the liquid evaporates, until the rice is al dente and the sauce is thick but still slightly soupy, 15 to 20 minutes.
When the rice is almost done, in between stirrings, heat the olive oil in a large frying pan over medium-high heat. Add the squid, scallops, prawns, and mussels, and cook for 2 minutes, stirring occasionally. Add the remaining ½ cup white wine and cook for another minute.
When the rice is still just a little bit al dente, mix in the cheese. Fold in the chive butter and whipped cream, and taste for seasoning. Serve in warmed soup plates, with the seafood and its juices on top of the rice.