Dry the Scallops: Pat the scallops thoroughly dry with paper towels. Removing excess moisture helps them develop a deep golden crust instead of steaming in the skillet.
Season the Scallops: Place the scallops on a large plate. Season both sides evenly with the salt and black pepper.
Heat the Skillet: Heat a large cast-iron skillet over medium-high heat for about 2 minutes. Add 1 tablespoon of the olive oil and swirl it around the skillet.
Sear the First Side: Arrange the scallops in a single layer, leaving a little space between them. Cook without moving them for about 2 minutes, or until the bottoms are deeply golden.
Cook the Second Side: Turn the scallops with tongs and cook for another 1 to 2 minutes. The scallops should be browned outside and opaque but still tender in the center. Transfer them to a clean plate.
Add the Lemon Rind: Reduce the heat to medium. Add the finely grated lemon rind to the skillet and stir for about 15 seconds, just until fragrant.
Add the Lemon Juice: Pour in the lemon juice, scraping the bottom of the skillet to loosen the browned bits. Let it bubble for about 30 seconds.
Add the Balsamic Vinegar: Pour in the balsamic vinegar and simmer for about 15 seconds.
Add the Remaining Oil: Stir in the remaining 1 tablespoon olive oil to bring the pan mixture together.
Cook the Garlic: Add the minced garlic and cook for about 30 seconds, stirring constantly so it does not burn.
Cook the Tomatoes: Add the grape tomatoes and stir to coat them in the lemon-balsamic mixture. Cook over medium heat for 3 to 4 minutes, or until the tomatoes are hot, glossy, and beginning to soften.
Spread the Pesto: Spoon the pesto onto a serving platter and spread it into an even layer.
Plate the Scallops: Arrange the seared scallops over the pesto. Spoon the warm tomatoes and the pan juices around and between the scallops.
Finish with Basil: Sprinkle the sliced fresh basil over the scallops and tomatoes. Serve immediately while the scallops are warm and tender.