Add the potatoes to a large pot and fill with water several inches above the potatoes. Salt the water generously - about 1 tablespoon of salt per 8 cups of water. Bring to a boil. Boil until the potatoes are completely tender, approximately 15-20 minutes depending on the size. Reserve about 1 cup of the cooking water and then drain the potatoes. Once cool enough to handle, remove the peels.
Meanwhile, in a small saucepan or skillet, heat the olive oil and coconut oil over medium-low heat until the coconut oil is fully melted. Add the garlic, and cook, stirring frequently, for about 3 minutes or until the mixture is a little frothy and the garlic is just starting to get some color. Remove from the heat.
Add the cooked potatoes to a mixing bowl and mash them using an extruding masher (or a ricer if you're so lucky). Mash them just until smooth, about 2 minutes. Stir in the oil and garlic mixture, just until evenly combined. Then, stir about 1/3 to 1/2 cup of the reserved potato cooking water, a little at a time, until the desired texture is reached. If using, stir in the chopped parsley.
The final step is to season your vegan mashed potatoes to taste with salt and pepper. The potato water is salted heavily, but I often find that these still need another good dose of salt to really bring out the earthy flavor of the potatoes. If you're unsure if they're salty enough, they're probably not salty enough! Finally, serve warm with a great vegan gravy.
Notes
POTATO TYPE AND PREP: I most highly recommend a blend of 1 lb. Yukon gold potatoes and 1 lb. of Russets. However, you can use either, or another type of potato if you prefer. Just don't use a waxy potato like red bliss. When cutting your potatoes up to boil them, cut them into pretty big pieces. When using a mix of Russets, which are larger, and Yukons which are smaller, I often quarter the Russets and halve the Yukons so that all pieces are a similar size.