Trim the fat from the steak, and cut the meat into 1-inch cubes.
Combine the flour and pepper, and dredge the meat in the flour mixture, reserving the excess.
Cook the meat, 3/4 cup chopped onion, and the reserved flour mixture in oil in a Dutch oven over low heat until the meat is lightly browned.
Add the water, 1/2 cup finely chopped carrots, celery, parsley, salt, and thyme. Cover, reduce the heat, and simmer for 1 1/2 hours.
Add the potatoes, 1 cup sliced carrots, and 1 cup chopped onion. Cover and simmer for 20 minutes.
Add the peas and cook for an additional 10 minutes.