Once the cod has soaked for the requisite time, remove from the water and pat dry. With a very sharp fillet knife, slice the cod into very thin slices and set aside.
In a small, non-reactive bowl, combine the herbs and oven-roasted tomatoes and toss with the lemon juice, olive oil and salt and pepper, to taste.
Divide the baccala evenly among 4 chilled dinner plates. Top each serving with a mound of the salad, drizzle with best-quality extra virgin olive oil and balsamic vinegar.
Preheat oven to 250 degrees. Toss all ingredients together and place flesh side up on a rack sitting on a sheet pan. Roast in oven for 2 to 3 hours until tomatoes dehydrated yet still tender.