Heat oil with 1 tsp. butter in medium non-stick skillet over medium-high heat. Sauté leek and onion until they start to brown, about 5 minutes. Add half the cabbage, stirring and turning until coated with oil and wilted, about 4 minutes. Continue adding cabbage a handful at a time, until it is all wilted, about 8 to 10 minutes. Pan will be very full.
Pour in half the broth and bring to a boil. Reduce heat and simmer until cabbage absorbs broth, about 15 minutes. Add remaining broth. Cook until cabbage is soft, about 15 minutes.
Meanwhile, place potatoes in saucepan and cover with 2 inches of cold water. Bring to boil over high heat, cover, reduce heat and cook until just tender, about 15 minutes. Drain potatoes and cut them in half.
Mix cooked potatoes into cabbage. Season with salt and pepper. Transfer mixture to a serving bowl. Dot top with remaining butter, cut into small pieces. Mix to combine and melt butter. Serve immediately.