Place potatoes in a large saucepan; cover with water. Bring to a boil. Reduce heat; simmer 20 minutes or until tender. Drain and return to pan. Mash potatoes with a potato masher.
While potatoes cook, bring 4 cups water to a boil in a large Dutch oven. Add cabbage; cook 5 minutes or until tender. Drain in a colander over a bowl, reserving 1/2 cup cooking liquid. Combine cabbage and reserved cooking liquid in a food processor; process until smooth. Add cabbage to potatoes; cook over medium-high heat 3 minutes or until thoroughly heated, stirring constantly. Stir in the salt and oil.