1. Bring a large saucepan of lightly salted water to a boil over high heat. Add the carrots and boil for 5 minutes. Add the parsnips and potatoes, and boil for 25 minutes longer, or until the vegetables are very tender. Drain well, shaking off any excess water.

2. Put the vegetables and olive oil in a food processor, and process to a puree. With the motor running, slowly add the milk or cream. Transfer to a bowl, stir in the tarragon and season with salt and pepper. Serve hot.