Adjust oven rack to lowest position and heat oven to 375 degrees.

Pat dry 1 pound chicken thighs, trimmed and halved, with paper towels.

Whisk the thinly sliced whites of 3 scallions, 8 teaspoons low-sodium soy sauce, 2 tablespoons Shaoxing wine, 4 teaspoons oyster sauce, 2 teaspoons grated ginger, and ½ teaspoon white pepper together in large bowl.

Measure out ¼ cup sauce and transfer to small bowl; set aside until ready to serve.

Whisk 3 minced garlic cloves into remaining sauce in large bowl, then add chicken and toss to coat.

Heat ¼ cup avocado oil in Dutch oven over medium-high heat until shimmering.

Add chicken and cook until golden, 4 to 6 minutes, stirring occasionally; using slotted spoon, return chicken to bowl.

Add 2 cups water and 1 cup unsalted chicken broth to fat left in pot, scraping up any browned bits.

Cover pot and bring to boil over high heat.

Off heat, stir in 1½ cups rinsed long-grain brown rice and 1 teaspoon table salt, spread chicken and any accumulated juices in single layer over rice, then top with 8 ounces shiitake mushrooms, stemmed and sliced ¼ inch thick.

Cover, transfer pot to oven, and bake until rice is tender and top of rice is dry and beginning to brown, 60 to 70 minutes.

Remove pot from oven, place clean dish towel under lid, and cover pot tightly. Let rest for 10 minutes.

Remove towel and lid from pot. Cook over medium-high heat until rice on bottom is crackling, about 2 minutes.

Drizzle reserved sauce over chicken and sprinkle with thinly sliced greens of 3 scallions. Serve.