Pat sea scallops dry with paper towels. Season with some lemon juice, salt, and pepper on one side.
Heat olive oil in a skillet over high heat. Place scallops in the skillet seasoned-side down. Cook until browned on the bottom, about 2 minutes. Season with remaining lemon juice, salt, and pepper; flip. Continue cooking until opaque, about 2 minutes more. Top with beurre blanc and serve!
Boil wine, vinegar, and shallot in a 2- to 3-quart heavy saucepan over moderate heat until liquid is syrupy and reduced to 2 to 3 tablespoons, about 5 minutes. Add cream, salt, and white pepper and boil 1 minute. Reduce heat to moderately low and add a few tablespoons butter, whisking constantly. Add remaining butter a few pieces at a time, whisking constantly and adding new pieces before previous ones have completely liquefied (the sauce should maintain consistency of hollandaise), lifting pan from heat occasionally to cool mixture.
Remove from heat, then season to taste with salt and pepper and pour sauce through a medium-mesh sieve into a sauceboat, pressing on and then discarding shallot. Serve immediately.