Put the quail eggs in a small pot, cover with cold water and bring to the boil. Reduce the heat and boil gently for 3 minutes. Turn off the heat, leave the eggs in the water for three more minutes then rinse in cold water. Let cool the eggs completely then peel them and cut in half. Transfer eggs, tomatoes and chives in a large bowl.
In the meantime, cook the Tortelloni according to package instructions, drain and transfer to the bowl. Season with salt, pepper, and drizzle generously with oil. Mix gently, divide among plates and serve.