Olive oil mashed potatoes are smooth, creamy, and rich enough that no one will ever miss the dairy.
In a large pot, add enough cold water to cover the potatoes by 1 inch. Add 1 tbsp. salt. Bring to a boil and cook until very tender, 12 to 15 minutes.
Meanwhile, in a small saucepan, heat 2/3 cup oil, the garlic, rosemary, lemon zest, crushed red pepper, and 1/8 tsp. salt over low, stirring occasionally, until bubbling, 1 to 2 minutes.
Reserve 1 cup of the potato cooking water; drain the potatoes. Push the potatoes through a potato ricer back into the pot, or return the potatoes to the pot and mash with a potato masher. Strain the oil mixture into thepotatoes and add 1/2 cup of thereserved cooking water, mixing inmore cooking water if thepotatoes are too thick; season.Transfer the potatoes to a bowl, drizzle with oil, and sprinkle with the parsley.