Heat the avocado oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the diced yellow onion and sauté, stirring occasionally, until softened, about 5 minutes.
Stir in the uncooked brown rice and minced garlic and cook, stirring, for about 3 minutes to toast the rice slightly.
Add the lemon zest, lemon juice, chopped rosemary, and chicken broth; stir to combine.
Carefully place the chicken thighs into the pot in a single layer so they are partially submerged but not overlapping.
Cover the pot and bring to a full boil, then reduce heat to low, cover, and simmer for 40 minutes.
Remove the lid, add the broccoli florets, replace the lid, and cook an additional 5 to 10 minutes until the rice is tender and the broccoli is cooked to your liking.
Serve the chicken, rice, and broccoli hot; optionally sprinkle grated Parmesan over the rice before serving.
