In a medium saucepan, cover red potatoes with water. Bring to a boil and then reduce heat to low; simmer for 15 minutes or until easily pierced with fork.
While potatoes are cooking, heat oil in a medium skillet over medium heat. Add leeks and sauté until softened and just beginning to brown, about 10 minutes.
Combine potatoes and soymilk in a large bowl. Using a potato masher or potato ricer, mash until potatoes reach desired consistency (I like mine chunky!). Fold in leeks and season with salt and pepper.
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