In a small bowl, whisk the creme fraiche with the finely grated lemon zest, fresh lemon juice, snipped chives and 1 tablespoon of the olive oil. Season the lemon-chive creme fraiche with salt and pepper.
In a medium skillet, heat the remaining 2 tablespoons of olive oil until shimmering. Generously season the scallops with salt and pepper and add them to the skillet. Cook the scallops over moderately high heat, turning once, until they are golden and just cooked through, about 5 minutes. Transfer the scallops to a plate; tent with aluminum foil to keep warm.
Meanwhile, in another medium skillet, cook the pancetta over moderately high heat, turning once, until browned and crisp, about 4 minutes. Add the brussels sprouts and shallot and cook, stirring, until the brussels sprouts are softened but still bright green, about 2 minutes. Off the heat, stir in the butter and garlic and season with salt and pepper; transfer to plates and top with the scallops. Serve with the lemon-chive creme fraiche.