Make sure the side muscles are removed and pat the scallops dry. Season on both sides with 3/4 tsp salt and 1/2 tsp pepper.
Heat 1 Tbs. of the butter and the oil in a 12-inch skillet over medium-high heat until the foam from the butter subsides.
Add the scallops and cook, undisturbed, until well browned, 2-3 minutes. Flip and cook the second side until browned and just barely firm to the touch, 1-2 minutes. Transfer to a dish & cover to keep warm.
Add the remaining butter to the skillet. Add the shallot and 1/4 tsp salt; cook, stirring, until softened, about 2 minutes. Whisk in the juice and season to taste with salt and pepper.
Serve scallops over wilted greens or with herbed couscous. Drizzle with the sauce and add black pepper to taste.