Cook the spaghetti according to package directions until al dente. Drain through a sieve.
Cut the fillet into small, fine strips.
Briefly rinse the arugula under running water and cut into bite-sized pieces. Heat the oil in a pot until very hot.
Add the filet and sauté until hot, about 1 1/2 minutes. Turn the heat down to medium. Now add tomato paste to the fillet and add enough water to make a sauce that is not too runny. Add balsamic vinegar and the arugula to the sauce and season with a little salt and a lot of pepper. Arrange the spaghetti with the sauce on plates and serve sprinkled with freshly grated Parmesan cheese.
