Bring rice and 2 1/2 cups broth to a boil in a covered saucepan. Reduce heat to low, cook for 18 minutes and rest off heat, covered, for 10 minutes.
Heat oil in a large skillet over medium-high heat. Brown beef for 7 to 8 minutes, breaking it into small crumbles and cooking to 160°F; leave about 1 tablespoon fat in the pan.
Add liver, onion, celery and bell pepper. Cook for 8 to 10 minutes, stirring and breaking up the liver until the vegetables soften and the liver reaches 165°F.
Stir in garlic, thyme, sage, white pepper, cayenne and salt for 1 minute. Add the remaining 1/2 cup broth and water and scrape up browned bits.
Simmer for 4 to 5 minutes until only a little moist liquid remains between the meat and vegetables. Fluff the cooked rice and fold it gently into the skillet.
Cook over medium-low heat for 3 minutes, folding once or twice, until the grains absorb the pan juices. Stir in scallions and serve hot.