In a blender on high speed, combine mustard, lemon juice, vinegar, and ginger for just a few seconds until smooth. Then turn the blender to a lower speed and slowly pour the oil in a continuous stream. Season with salt and pepper, to taste.
Place shredded lettuce piled high in the center of a bowl with edges. Add dressing to lettuce and toss. Sprinkle parsley around the edges of the bowl and garnish with a lemon slice.