To prepare stew, heat oil in a large Dutch oven over medium heat. Add onion; cook 5 minutes or until golden, stirring frequently. Add celery, salt, and mushrooms; cook 3 minutes, stirring frequently. Add broth, peas, oregano, pepper, and bay leaf; bring to a boil. Reduce heat, and simmer, partially covered, 45 minutes or until peas are tender. Add tomatoes; return to a boil. Reduce heat, and simmer, partially covered, 15 minutes. Discard bay leaf.
To prepare dumplings, while stew is simmering, combine cornmeal and next 4 ingredients (cornmeal through sugar) in a bowl, stirring with a whisk. Stir in buttermilk, butter, and egg; let stand 10 minutes.
Drop dough by tablespoonfuls into stew to form 15 dumplings. Cover and cook 15 minutes. Garnish with parsley, if desired.