Prepare a grill or heat up a grill pan. If available, place a piece of slate on the grill and heat for at least 5 minutes.
Meanwhile, place the rabbit on a platter and season with salt and pepper. Drizzle 3 tablespoons of olive oil over and scatter garlic slices from 3 cloves, 8 sprigs of thyme and 4 sprigs of rosemary (halved to make 8). Allow it to marinate while the grill is heating.
When the slate is hot, place the rabbit pieces on the slate. Cook on each side until the rabbit is nicely seared and cooked through, about 5 to 7 minutes per side. Remove the garlic cloves and discard if they begin to burn, they will give a harsh flavor to the rabbit.
Season the vegetables with salt and pepper and drizzle with olive oil. Halfway into cooking the rabbit, place the vegetables on the slate and place a sprig of thyme and rosemary and a few slices of garlic on each. Cook on each side until nicely browned and softened, about 2 to 3 minutes per side. Serve hot or room temperature.