In a stock pot, bring water and 2 teaspoons salt to a boil. Add turnip greens and potatoes and boil gently, uncovered, until just tender, about 17-20 minutes.
Meanwhile, melt butter in a 12-inch non-stick skillet over medium heat and saute mushrooms until tender, about 7-10 minutes. During the last minute of cooking time, add marjoram, brown sugar and crushed garlic. Remove from heat when done cooking.
When potatoes and greens are done, drain in a colander and add potatoes and greens to the mushrooms. Stir to combine and cook for another 5 minutes or so, to heat through.
Season to taste with salt and freshly ground pepper.