In a large saucepan, combine the potatoes, 1 teaspoon salt, and cold water to cover. Bring to a boil over high heat. Lower the heat to maintain a simmer and cook until fork tender, about 10 minutes. Drain the potatoes, reserving a 1/2 cup of the cooking liquid. Return potatoes to the pan. Shake the pan over medium heat for about a minute to dry the potatoes. Transfer the potatoes to a food mill, ricer, or bowl.

Add the oil and reserved cooking liquid to the saucepan, and warm over medium heat. Remove pan from the heat. Mash the potatoes through the food mill, ricer, or by hand into the pan. Add the herbs and stir to combine. Season with salt and pepper to taste. Serve immediately.