Start the rice: Rinse 1 cup rice under cold water until water runs clear. Cook according to package directions (usually 1 ¼ cups water, simmer 15 minutes, rest 5 minutes). While it cooks, make the chicken.
Make the glaze: In a small bowl, whisk together honey, lime juice, soy sauce, grated garlic, and grated ginger. Set aside.
Dry and season the chicken: Pat chicken thighs dry with paper towels. Season generously with salt and pepper.
Sear the chicken: Heat 1 tbsp oil in a large skillet over medium-high heat. Add chicken thighs in a single layer, smooth side down. Cook without moving for 5-6 minutes, until deep golden. Flip and cook 4-5 minutes more.
Glaze the chicken: Reduce heat to low. Pour the glaze into the pan around (not over) the chicken. Let bubble and reduce for 1 minute, spooning over the thighs as it thickens. Remove chicken to a cutting board and rest 5 minutes.
Make the crema: While chicken rests, stir together sour cream, lime zest, a pinch of salt, and enough water (2-3 tbsp) to make a drizzleable consistency.
Slice and assemble: Slice chicken against the grain into ½-inch strips. Divide rice among 4 bowls. Top with sliced chicken, sliced avocado, a drizzle of crema, flaky salt, and cilantro leaves. Serve immediately.