Remove the dark green portion of the leeks and discard. Cut the leeks in half lengthwise and wash in water, being careful to check all the layers for hidden dirt. Fill a wide pan with water about 1/2-inch high up the sides. Add the leeks, simmer gently for 12 minutes, and then drain.
Meanwhile, make the vinaigrette. In a small bowl, whisk together the mustard and balsamic vinegar, and then drizzle in the oil to make an emulsion, whisking constantly. Add in the salt, pepper, and thyme. Lay the leeks lengthwise on small serving platter. Sprinkle with the chopped bacon, drizzle with the dressing, and serve.