In a mixing bowl, whisk together honey, soy sauce, Sriracha, minced garlic, finely chopped onion, chicken broth, salt, and black pepper until combined to make the marinade.
Place the chicken thighs in the 9×13 casserole dish and pour the marinade over them, tossing to coat evenly. Cover with plastic wrap and refrigerate for at least 30 minutes and up to 24 hours.
Preheat the oven to 425°F (220°C).
While the chicken marinates (or when ready to cook), rinse the rice under cold water until the water runs clear. In a heavy-bottomed pot, combine the rinsed rice with 2 cups water, bring to a boil, then reduce heat to low, cover, and simmer for 12–15 minutes until the water is absorbed. Remove from heat and let sit, covered, 5–30 minutes; then fluff with a fork.
To steam the broccolini, bring a few inches of water to a boil in a pot fitted with a steamer basket (water should not touch the basket). Add broccolini, cover, and steam 4–6 minutes until tender-crisp. Remove and set aside.
Remove the plastic wrap from the casserole dish and bake the chicken uncovered in the preheated oven for 20 minutes.
If you prefer a crispier exterior, switch the oven to broil and broil the chicken 2–3 minutes more, watching carefully to avoid burning the honey glaze.
Serve the chicken thighs over the cooked rice with steamed broccolini on the side, spooning any pan drippings over the chicken and rice, and garnish with chopped parsley.