In a food processor fitted with the 2-mm slicing blade, shred the Brussels sprouts.
Heat 2 Tbs. of the oil in a 12-inch nonstick skillet over medium-high heat until shimmering hot. Add the Brussels sprouts, season with salt and pepper, and toss to coat with the oil. Cover and cook until starting to soften, about 1-1/2 minutes. Transfer to a platter and keep warm.
Season the scallops with salt and pepper. Dust both flat sides with all-purpose flour. Heat the remaining 1 Tbs. oil in the skillet over medium-high heat until shimmering hot. Add the scallops and cook, flipping once, until browned and just cooked through, about 5 minutes.
Put the scallops on top of the Brussels sprouts and return the skillet to medium-low heat. Add the butter, lemon juice, mustard, and 2 Tbs. water and cook, stirring and scraping up any browned bits, until the butter is incorporated and the sauce has thickened, about 1 minute. Season to taste with salt and pepper, spoon over the scallops, and serve.