Remove the large center stems from the collard greens. Stack the leaves on top of each other and roll them as tightly as possible. Use a sharp chef's knife to slice the leaves as thinly as possible.
Use a vegetable peeler to remove three 1-by-2-inch strips of peel from the lime. Finely chop the peel.
Heat the olive oil in a large, wide pot over medium heat. Add the ginger, garlic, mustard, jalapeno and 1/2 teaspoon salt and cook, stirring occasionally, until very fragrant and the garlic is pale golden, about 3 minutes. Add the vinegar and simmer until almost completely reduced. Increase the heat to medium-high and add the collard greens. Cook, tossing with tongs, until just slightly wilted, about 3 minutes. Serve warm.