Bring the broth to a boil, add broccoli, and simmer until the broccoli is just tender. In a saucepan, saute onions in olive oil then stir in ginger and rice and stir to coat with oil. Stir one cup of broth from the broccoli into the rice until it is absorbed. Gradually add remainder of broth and broccoli, cooking until the rice is just done, about 15 minutes. Remove from heat, add lemon juice, feta, and Parmesan, and serve immediately.