Heat a large skillet with sides over medium-high heat and add olive oil. Once fragrant, add the minced onion. Season with ⅛ teaspoon of salt and sauté for 3 minutes.
Add minced garlic to the skillet and sauté for another minute before adding orzo pasta. Toss the orzo with onion and garlic and toast for 3-4 minutes until golden brown, stirring consistently.
Add remaining salt, chives, black pepper, broth, milk, and hot sauce to the skillet. Stir and bring to a gentle boil, then reduce heat to low and cover. Simmer orzo for 3-4 minutes.
Uncover the skillet and add chopped broccoli. Gently toss with orzo, cover, and simmer for another 3-4 minutes until most liquid is absorbed.
Remove skillet from heat, add cheddar cheese, and stir until melted.
Serve immediately, garnished with freshly cracked pepper.