Soak baccala in water for 2 days in the refrigerator, changing the water occasionally. Drain, and cut into 2-inch pieces.
Mound flour in the center of a large board. Make a well in the middle, and add eggs and 1 tablespoon oil. Using a fork, beat eggs and oil until thoroughly combined. Begin to incorporate flour, starting with the inner rim of the well. The dough will come together when half the flour is incorporated. Keep working dough until all flour is incorporated.
Start kneading dough using the palms of both hands. Once dough is a cohesive mass, remove it from the board; scrape up and discard any leftover bits. Lightly flour the board, and continue kneading for 6 minutes more. The dough should be elastic and slightly sticky. Wrap the dough in plastic, and allow to rest for 30 minutes at room temperature.
Place baccala in the bowl of a food processor, and pulse until it is broken up but not completely smooth. Transfer fish to a large bowl, and add riced potato, 3/4 cup olive oil, rosemary, and chives. Stir well to combine. Season with salt and pepper; set aside.
Divide pasta into 2 pieces. Working quickly, roll out each sheet of pasta to the thinnest setting on a pasta machine, and place on a lightly floured board. If using a ravioli pin: Cover the pasta with a 1/4-inch-thick layer of the fish mixture. Place a second sheet of pasta over it, and press down lightly with your hands. Lightly flour the ravioli pin. Carefully roll the 2 sheets together with the ravioli pin, forming the ravioli. Use the dull edge of a knife to seal the edges together. Cut ravioli to separate. Transfer to a baking sheet dusted with semolina.
If not using a ravioli pin: Cut a single sheet of pasta at a time into 2 by 1-inch rectangles. Place a teaspoon of the fish mixture into the center of each rectangle, and fold the pasta to form a 1-inch square, pressing the edges to seal. Repeat with remaining dough and filling.
Bring 8 quarts of water to a boil, and add 3 tablespoons salt. Drop in ravioli, and cook until tender, 6 to 7 minutes. Meanwhile, in a large saute pan, combine tomato sauce, thyme, red-pepper flakes, and mint. Add remaining 3 tablespoons oil, and place over medium heat. Drain ravioli, reserving a cup of the cooking water; add ravioli to the pan with the tomato sauce, and toss to coat. Adjust the consistency of the sauce with cooking water, and serve immediately.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic, and cook until soft and light golden brown, 8 to 10 minutes. Add the thyme and carrot, and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and reserved juice, and bring to a boil, stirring often. Lower the heat, and simmer for 30 minutes until thick. Season with salt. The sauce can be stored in the refrigerator for 1 week or up to 6 months in the freezer.
Yield: 4 cups