Heat olive oil in a large pot over medium heat.
Add diced onion and sauté for 3-4 minutes until translucent.
Add minced garlic and cook for 30 seconds until fragrant.
Add rice to the pot and stir to coat the rice with the oil, cooking for 1-2 minutes.
Pour in vegetable broth and stir in salt, black pepper, dried thyme, and crushed red pepper flakes if using.
Bring the mixture to a boil, then reduce heat to low and cover the pot with a tight-fitting lid.
Simmer for 10 minutes.
After 10 minutes, add the broccoli florets on top of the rice without stirring.
Cover and continue to cook for another 10-12 minutes until the rice is tender and the broccoli is cooked but still bright green.
Remove the pot from heat and let it sit covered for 5 minutes.
Fluff the rice and broccoli gently with a fork.
Stir in grated Parmesan cheese until melted and combined.
Serve warm.