Blot the scallops very dry, pull away the small side muscle if present, and season with salt and pepper just before cooking. The scallops should feel dry to the touch rather than slick or wet.
Heat a large skillet over high heat, then add the olive oil and 1 Tablespoon butter before arranging the scallops with space between each one. They should make a gentle, immediate sizzle when they meet the pan.
Leave the scallops in place for 2 minutes without nudging or turning them. A deep golden ring should develop where each scallop touches the skillet.
Lower the heat to medium-high and turn each scallop with tongs, then cook the second side for 1 to 2 minutes. The sides should look partly opaque while the center remains tender and lightly translucent.
Press one scallop lightly and remove the batch from the pan when it feels firm with a small spring back. Residual heat will continue to finish the center as the scallops rest.
Set the scallops aside, then add 2 tablespoons butter, 3 to 4 cloves garlic, juice from half a lemon, and ¼ cup white wine, chicken or vegetable broth to the skillet; cook for 2 minutes while scraping up the browned bits. The sauce should smell garlicky and bright, with the browned bits dissolved into the butter.