Preheat the oven to 375 degrees. In a large oven-safe pot or Dutch oven, melt the butter over medium heat on the stovetop.
Add the diced onion and cook for 3 minutes until it softens. Stir in the minced garlic and cook for 1 minute more.
Add the orzo and stir to coat it in the butter. Pour in the chicken broth and bring the mixture to a boil.
Reduce the heat to a simmer, cover the pot, and cook for 8 minutes, stirring once halfway through.
Stir in the broccoli florets, salt, and pepper. Cover and cook for 4 more minutes until the broccoli is tender.
Remove the pot from the heat and stir in the milk and 1 cup of the shredded cheddar until the cheese melts and the mixture turns creamy.
Sprinkle the remaining 1/2 cup of cheddar evenly over the top. Transfer the pot to the oven and bake uncovered for 10 minutes until the cheese is bubbly and lightly golden.