Heat four tbsp oil in a heavy large frying pan over medium-high heat. Working in batches, add the courgettes and fry until golden, about two minutes per side. Using a slotted spoon, transfer the fried courgettes to a baking dish. Sprinkle generously with salt and pepper. Sprinkle half of the garlic, basil, and mint leaves over the courgettes.
Add the remaining oil to the frying pan. Add the carrots to the hot oil and saute until golden, about 5 minutes. Using a slotted spoon, transfer the fried carrots to the dish of courgettes. Sprinkle generously with salt and pepper. Sprinkle the remaining garlic, basil, and mint leaves over. Drizzle the vinegar over the vegetable mixture and toss gently to coat. Cool to room temperature.
Cover and marinate in the refrigerator overnight. Allow the vegetables to come to room temperature before serving. Transfer the scapece to a platter. Serve with bread, fish or chicken.