Rillettes are found throughout France. Traditionally made with pork or duck, and are essentially pulverized confit, shredded meat smashed with fat to produce a rich, rustic paste for spreading on bread. The meat is cooked slowly over low heat until very tender – this is the confit – then raked into small shreds and blended with the warm cooking fat to form a rustic paste. Rillettes, like confit were originally a means of preservation. The meat could be stored in crocks under a layer of fat in a cool place. These are shrimp rillettes and simply put, it's a shrimp spread or shrimp dip.
Heat the oil in a large skillet over moderate heat. Add onion and bay leaf. Cook until clear and translucent, about 3 minutes. Add the shrimp. Season with salt and pepper and cook, stirring occasionally, until shrimp are pink and cooked through, about 3 minutes. Remove and discard the bay leaf. Place the mixture in the bowl of a food processor fitted with the blade attachment.
Add the butter and cheese. Puree until smooth. Add lemon juice, chives, and salt and pepper to taste and transfer to a 1 1/2-cup crock, or to 3 small jars and cover with plastic wrap, pressing the plastic wrap directly onto surface of shrimp mixture. Refrigerate at least 8 hours to blend flavors or up to 3 days. Let stand 30 minutes at room temperature before serving.