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