Brown the chicken breast in the butter, seasoning it with salt and pepper; set aside. Chop mortadella finely and combine in a bowl with the chicken, ricotta, 1 cup grated Romano, 1 egg, nutmeg, salt and pepper, and mix well.
Heap the flour in a mound on a board and make a well in the center. Break in the 2 remaining eggs and knead into soft, smooth dough. Roll out into a thin (1/8" thick) sheet and cut into 1-1/4" circles (you can use a small juice glass).
To make tortellini, place a little of the filling in the center of each circle and fold the pasta in half, pressing it around the edges to seal in filling. Then wind the folded edge around the tip of your index finger and press the 2 ends together to form a ring.
Bring chicken broth to a simmer.
Bring the stock to a boil. Drop in tortellini and cook until al dente, about 3-4 minutes. Drain and serve in bowls of broth, passing remaining grated cheese.