In a large pot, bring salted water to a boil. Add the orzo pasta and cook according to package instructions until al dente, about 8-10 minutes. During the last 3 minutes of cooking, add the broccoli florets.
Once cooked, drain the orzo and broccoli in a strainer and set aside.
In the same large pot, heat the olive oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant, being careful not to burn it.
Pour in the vegetable broth and bring the mixture to a gentle simmer. Allow it to cook for about 5 minutes to develop flavor.
Reduce the heat to low, then add the cooked orzo and broccoli to the pot. Stir to combine, ensuring the orzo is well coated with the broth.
Gradually mix in the shredded cheddar cheese and grated Parmesan cheese until melted and creamy. Adjust seasoning with salt and pepper to taste.
Remove from heat and serve warm. If desired, sprinkle red pepper flakes on top for a bit of heat.