In a large saucepan, heat the 1 tablespoon of olive oil. Add the reserved lamb trimmings along with the chopped carrot, celery and onion and cook over moderately high heat, stirring, until lightly browned, about 10 minutes. Add 1 tablespoon of the chopped garlic and the chopped tomato and cook until softened, about 5 minutes. Add the red wine and bring to a boil. Add the low-sodium beef broth and the reserved parsley and thyme stems and simmer over moderate heat until reduced to 1 1/4 cups, about 1 hour. Strain the lamb sauce into a small saucepan and spoon off the fat. Season the sauce with salt and pepper and keep warm.
Preheat the oven to 400°. Light a grill or preheat a grill pan. In a small bowl, combine the chopped parsley, chopped thyme and the remaining 2 tablespoons of garlic. Season the lamb racks with salt and freshly ground black pepper and coat with the herb mixture. Drizzle the lamb with olive oil and oil the grill or the grill pan. Grill the lamb over moderately high heat, turning once, until browned all over, about 5 minutes. Transfer the racks to a sturdy baking sheet.
Roast the racks of lamb for about 15 minutes, until an instant-read thermometer inserted in the center of the meat registers 130° to 135° for medium-rare. Let the racks rest for 15 minutes.
In a medium skillet, toast the pine nuts over moderate heat, stirring, until they are golden, about 5 minutes. Let the toasted pine nuts cool slightly. Transfer the toasted pine nuts to a blender. Add the parsley leaves, garlic and grated lemon zest and pulse to combine. Add the olive oil and process until smooth. Season the gremolata pesto with salt and pepper.
Reheat the sauce. Carve the racks of lamb into chops and serve the chops with the sauce and pesto.