Sounds like a somewhat Americanized version of Stracciatella:
6 cups reduced-sodium chicken broth
1/2 cup freshly grated Parmesan cheese
1/2 cup fresh bread crumbs
Salt and freshly ground black pepper, to taste
Additional freshly grated Parmesan cheese, for garnish
Bring the broth to a simmer in a Dutch oven or large saucepan. Crack the eggs into a medium bowl and beat well. Add the cheese and breadcrumbs and beat again. Ladle ½ cup of the hot stock into the eggs. Bring the stock up to a boil and whisk in the egg mixture. Reduce heat and cook for 3 to 4 minutes. Season to taste with the salt and pepper, ladle into bowls and top each serving with more Parmesan cheese, if desired.
Makes 6 1-cup servings.
In Italy, sometimes ground semolina (wheat) is used instead of breadcrumbs. The classic technique, from which the name is derived (I think it means to "scratch"), involves combining the stock and the egg/breadcrumb/cheese mixture in such a way that the mixture forms small clumps or strands in the broth which do resemble noodles. This, however, is not easy for the unpracticed to do--you tend to end up with a mess. So I think what your friend's mom was doing was making it easier--creating the "noodles" first and then adding them to the soup.