As you wait for the water to boil, drizzle 1 tablespoon extra virgin olive oil in the same pot used to make the chicken. Turn the heat to medium. Once hot, add the diced onion and sauté for 5 to 6 minutes. Add the reserved garlic paste and stir to coat the onions in the paste.
Add the broccoli and season with salt, pepper, and ½ teaspoon crushed red pepper. Sauté for 4 to 5 minutes until bright green. Be careful not to overcook the broccoli.
Add the shredded chicken and 1 tablespoon of flour to the broccoli. Toss to coat and cook for 1 minute.
Pour in 2 cups of the reserved homemade chicken broth and bring to a boil. Reduce the heat to low and add the cheddar cheese. Stir constantly until the cheese melts into the broth and the sauce is very smooth. Continue simmering until the broccoli is fork-tender.
Add the cooked orzo and turn off the heat. Stir to coat. Taste and adjust the seasonings to your preference. Let stand for 5 minutes.