For the beurre blanc

1. Boil wine, vinegar, and shallot in a medium saucepan over medium heat until reduced to 3 tablespoons, 10-15 minutes. Remove from heat and let cool slightly, about 30 seconds.
2. Turn on the heat to very, very low (just enough heat to keep the mixture warm but not hot). Place the saucepan over the heat. Add a few cold butter cubes to the reduced shallot-wine mixture and whisk until the butter is almost completely incorporated. Continue adding the butter a few cubes at a time and whisking until the mixture is the consistency of thick heavy cream. Stir in tarragon, half the lime pearls, and salt and pepper to taste. Set sauce aside.

For the scallops

1. Pat scallops dry on all sides with paper towels. Let scallops sit at room temperature for 5 minutes to allow the surface of the scallops to dry out (this will help the scallops get a nice sear).
2. Heat a heavy non-stick pan over medium-high heat. Add enough oil to coat the bottom of the pan, 1-2 tablespoons. Swirl the pan so that the bottom is evenly coated with oil. When oil starts to shimmer, add the scallops and sear scallops until underside is golden brown, about 2 minutes. Gently turn scallops over and sear the other side until golden brown and scallops are just cooked through, about 2 minutes more.

To serve

1. Divide scallops among 4 plates. Spoon sauce over scallops and top each scallop with some of the remaining lime pearls.