Olive Oil Mashed Potatoes (No Milk, No Butter)

0 Prep the potatoes: Wash them, and trim off any eyes or damaged skin. Peel if you prefer smoother mashed potatoes. Slice them so they're all about the same size, about 2-inches in diameter. Leave them whole if they're golf-ball size.
1 Put the potatoes in a large pot of water and add 3 tablespoons of the salt. Bring to a boil, then reduce the heat to a simmer. Cook until the potatoes are fork tender, but not falling apart, 20-25 minutes.
2 Scoop out 2 cups of the cooking water, then drain the potatoes and transfer to a large bowl. Pour the olive oil over and 1 cup of the cooking water. Mash them with a handheld potato masher, adding more water a little at a time until the potatoes are the texture you like (you might not use all the water). Taste and add more salt, if desired.
3 Serve warm, drizzled with additional olive oil.