What's the best way to make vegan mashed potatoes? I have vegan "butter" if that helps.
I use vegan butter and plain or unsweetened soymilk. Most people can't tell the difference, especially if you roast a few cloves of garlic and mash those into them as well. Dashes of rosemary and salt don't hurt either.
Making a rich vegetable stock to sub in for the milk/cream would probably do more for the flavor than vegan butter. You could also thread in caramelized onions and/or roasted garlic, a la this recipe: http://bit.ly/bChAIB
I actually love olive oil mashed potatoes, too - just beat or whip it in while you finish mashing until you have the texture you want.
Just season well the water the potatoes cook in with salt, pepper, some garlic to cook along with the potatoes, perhaps some herbs. Then, when you drain the potatoes, reserve the water (which has become vegetable broth). When you mash the potatoes, beat the warm liquid back in. You won't even need oil or "butter," but you could add it if you wish.
My husband doesn't like butter in his mashed potatoes (I know...go figure) so I recently gently poached several garlic cloves in olive oil for a long time till they were soft (like making a confit) and mashed them and the olive oil in with the potatoes. I stirred in a little of the potato water to thin them. Lots of salt and pepper. They were really good!
I like to use a combo of olive oil and stock.