For the marinated cherry tomatoes: Toast the coriander seeds in a small skillet over medium heat until fragrant, 3 to 5 minutes. Transfer to a mortar and pestle and crack. Allow to cool.
Bring a medium pot of water to a boil. Make a small "x" incision at the bottom of each tomato. Blanch the cherry tomatoes for 1 minute and immediately transfer them to a large bowl filled with ice water (an ice bath). Allow the tomatoes to cool, and then peel the tomatoes and discard the skins.
In a medium bowl, mix together the coriander, peeled tomatoes, onions, olive oil, ginger juice, basil, mint, vinegar, and garlic. Season with salt and pepper, cover, and allow the tomato mixture to sit at room temperature for 4 hours.
For the chicken: Combine the olive oil, basil and garlic in a large bowl. Add the chicken breasts, making sure to coat all sides with the marinade. Cover and let marinate for at least 2 hours in the refrigerator.
Preheat the grill to medium heat. Remove the chicken from the marinade and pat dry with a towel. Sprinkle with salt and pepper. Add chicken breasts and grill for around 5 minutes on each side, depending on how hot your grill is, or until cooked through.
Serve the chicken with some of the marinated tomatoes on top.