Directions

1. Process basil, 1/2 cup olive oil, and garlic in a food processor until basil is finely chopped, about 1 minute. Transfer mixture to a small bowl, and stir in 1/4 teaspoon kosher salt. Set basil oil aside until ready to use.
2. Stir together vinegar, sugar, 1/2 tablespoon coriander seeds, and 1/2 teaspoon kosher salt in a saucepan. Bring to a boil over medium-high, whisking to dissolve sugar. Stir in yellow grape tomatoes, and remove from heat. Let cool to room temperature, about 20 minutes. Strain and discard liquid. Set pickled tomatoes aside.
3. While tomatoes marinate, preheat grill to high (450°F to 500°F). Place remaining 1 tablespoon coriander seeds in a mortar, and pound and grind using pestle until coarsely ground. (Alternatively, crush coriander seeds using back of a heavy skillet.) Set aside. Drizzle chicken evenly with 1 tablespoon olive oil; sprinkle evenly with chopped thyme, crushed red pepper, 1/2 teaspoon black pepper, 1 1/2 teaspoons kosher salt, and reserved crushed coriander. Grill chicken on oiled grates until lightly charred on bottoms, 6 to 8 minutes. Flip chicken; grill until an instant-read thermometer inserted in thickest portion of each half registers 155°F, 5 to 7 minutes. Transfer to a platter, and let rest 5 minutes. (Temperature will continue to rise to 165°F.) Loosely cover chicken with aluminum foil to keep warm.
4. Drizzle cherry tomatoes on the vine with remaining 1 tablespoon olive oil; sprinkle evenly with remaining 1 1/2 teaspoons kosher salt and remaining 1/4 teaspoon black pepper. Grill tomatoes on oiled grates until they just start to wrinkle but have not yet burst, about 5 minutes. Transfer tomatoes to platter with chicken. Top with mozzarella and reserved pickled tomatoes. Spoon some of the basil oil over salad, and sprinkle with flaky salt to taste. Garnish with additional basil and thyme leaves. Serve alongside remaining basil oil.