Heat Olive Oil or Butter in a large deep skillet or Dutch oven over medium heat. Add onion and cook 3–4 minutes until softened.
Stir in garlic and cook 30 seconds.
Stir in salt, pepper, smoked paprika, and thyme.
Add the dry orzo and cook 1–2 minutes until lightly toasted.
Pour in chicken broth and bring to a gentle boil. Reduce heat to medium-low, cover loosely, and simmer about 8 minutes, stirring occasionally.
Stir in broccoli and continue cooking another 3–4 minutes until the orzo is tender and broccoli is bright green.
Lower heat. Stir in leftover chicken, milk, Dijon mustard, cheddar cheese, and parmesan until warmed through and creamy.
Notes
Store leftovers in a covered container in the refrigerator for 3 to 4 days. Reheat in the microwave in short intervals, or on the stove top over medium low heat.