04Drain tomatoes, reserving juice. Add tomatoes to vegetables in saucepan; raise heat and cook rapidly, breaking up tomatoes with a fork. Add rosemary or thyme, turn down heat and cook gently 20 to 30 minutes, until tomato sauce thickens. If necessary, add a little reserved juice to keep sauce from sticking.
05Remove mushrooms from the bowl, but do not discard the soaking water. Rinse mushrooms under running water from tap; chop coarsely and add to tomato sauce. Strain the soaking water through a fine-mesh sieve or a paper coffee filter directly into the sauce. Mix well. Taste sauce and add salt, if necessary, and freshly ground black pepper to taste.
06Slice sausages into 1/2-inch slices and add to the sauce, mixing well. Just before serving, remove rosemary sprig, if used. Serve over hot polenta mush or toasted or sauteed polenta slices.