Pat the scallops dry very well with paper towels then season lightly with salt.
Heat a large (10- to 12-inch diameter) sauté pan over medium-high heat and add oil. After 30 seconds, place half of the scallops in the pan (do not crowd pan and work in batches) and sear, undisturbed until well browned, about 3 minutes, then turn and cook other side until dark golden, about 2 to 3 minutes longer. Transfer scallops to a platter. Repeat with the remaining scallops then take pan off heat, discard oil and wipe pan clean.
Place the pan back on stove, heat to medium-high and add the butter. Once melted, let the butter bubble and froth and eventually brown, then quickly stir in the shallots and capers. Sizzle them in the butter until the shallots are slightly softened, about 1 minute, then stir in the thyme. Turn off the heat.
Serve the scallops immediately. Pour the brown butter sauce over the scallops, squeeze the lemon over them crack some freshly ground black pepper over the top, too.