Trim the carrots, parsnips, and leeks to 4 or 5 inches. Cut all into julienne strips.
Fill a large saucepan with water. Add ½ teaspoon salt and bring to a boil. Fill a large bowl with ice water. Place the carrots in small metal basket or strainer, submerge in the boiling water, and remove after 45 seconds. Follow with the parsnips at 30 seconds and the leeks at 10 seconds. As each vegetable comes out of the boiling water, plunge it directly into ice water, then drain. (A slotted spoon also works, if you lack the basket or strainer.)
After blanching, you can set the drained vegetables aside for hours. Finishing them in the herb butter is then a matter of a few minutes.
When you’re almost ready to serve, melt the butter in a large skillet over medium heat. Cook the shallots until translucent. Add the minced herbs, the scallions, and the blanched vegetables, turning them very gently in the butter. When they are heated through and tender, transfer to a warmed serving dish. Serve immediately.