In a large pot, bring 6 cups water and 2 teaspoons salt to a boil. Add mustard greens, stir down, return to a boil and boil gently for about 10 minutes. When done, drain in colander.
While greens are cooking, heat oil in a 12-inch non-stick skillet over medium-high heat. Add carrots and stir-fry for about 2 minutes. Add ginger and stir-fry for about 1 minute. Add scallions and garlic and stir-fry for another minute. Add hoisin sauce and sesame oil and stir to combine, then add drained greens and stir to mix well. Cook for another minute or two to heat through and evaporate any extra water that came from the greens.
Sprinkle cilantro leaves on top and serve immediately.