Mix the ingredients in the dressing in a food processor until blended, but not smooth. Pour into a bowl and set aside.
Assemble the ingredients for the noodles. Place 3 cups of noodles on the bottom of a large serving dish. Layer the romaines, carrots, eggs, and hams on top of the noodles. Pour the dressing on top of the assembled noodles when ready to serve. Lightly mix and serve.