Place the potatoes in a large pot and cover them with water. Bring to a boil over high heat, lower the heat to medium-low, cover, and simmer until fork-tender. This takes 20-30 minutes.
Drain the water and cover with cold (and/or iced) water. Let sit for 5-10 minutes, then peel.
Use a potato ricer to mash the potatoes and place them in a large bowl or pot. This is my favorite method. Alternatively, you can use a potato masher.
Add the melted butter or coconut oil, coconut milk, vegan sour cream, salt, and pepper. Mix thoroughly.
If using, add the parsley and/or garlic.