Gently warm the limoncello in a small saucepan over medium heat until steam begins to come off the top and it is hot to the touch but not simmering. Remove from the heat, then add the dried cranberries and cover with plastic wrap. Allow the cranberries to soak for at least 30 minutes or up to 1 hour. Drain and set aside.
Grate the carrots into a medium bowl using the large holes on a box grater. Sprinkle the carrots with the salt and toss well. Add the soaked cranberries, parsley leaves, lemon juice and olive oil and toss again to combine. Crumble the goat cheese over the top and serve.