Heat the olive oil in a large pot over medium heat.
Add the chopped onion and sauté for 3-4 minutes until translucent.
Add the minced garlic and cook for another 1 minute until fragrant.
Stir in the rice and cook for 1-2 minutes, stirring frequently to coat the rice with oil.
Pour in the vegetable broth and bring to a boil.
Once boiling, reduce the heat to low and cover the pot with a lid.
Cook the rice for 10 minutes.
After 10 minutes, add the broccoli florets on top of the rice without stirring.
Sprinkle the salt, black pepper, dried thyme, and red pepper flakes over the broccoli.
Cover the pot again and cook for another 10-12 minutes, or until the rice is tender and the broccoli is cooked through.
Remove the pot from heat and let it sit covered for 5 minutes.
Fluff the rice and broccoli with a fork, then stir in the grated Parmesan cheese.
Serve warm.