Saute rice in vegetable oil; add 4 cups water and salt; cook until 75% done. Drain and reserve 1½ cups of the water for later.
Saute onion in butter in soup pot until onion turns transparent; turn down heat. Mix flour in thoroughly, cook for 5 to 10 minutes, stirring often (do not let brown).
Using a whisk, blend in hot chicken stock and reserved rice stock. Allow soup to thicken slightly.
Add half and half, blending in thoroughly. Add rice, ham, salt, pepper, and rosemary. Simmer for 20 minutes.