Cover potatoes with water in a small pot; season with salt. Bring to a boil over medium-high heat, then reduce heat and simmer until 12 to 15 minutes until fork tender. Drain the potatoes.
While the potatoes are boiling. Melt 4 tablespoons of vegan butter in a large saucepan over medium heat. Add onions and cook, stirring frequently, until very soft, 8–10 minutes. Add garlic and cook, stirring frequently, until garlic is fragrant and onions are just beginning to brown around the edges, about 3 minutes longer. Add 1 cup cabbage and cook, stirring constantly, until wilted. Add oat milk and nutmeg bring to a simmer.
Add potatoes and remaining 1 cup cabbage, then coarsely mash with a potato masher. Season with salt and pepper.
Transfer colcannon to a large serving bowl. Top with remaining 2 Tbsp. butter and sprinkle with parsley.
Store leftover colcannon in a tightly sealed container. Colcannon will keep for 3 to 4 days in the fridge.