Heat olive oil in a large deep skillet or sauté pan over medium-high heat.
Season the chicken pieces with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the orzo pasta to the skillet and stir to coat it with the oil and onion mixture.
Pour in the chicken broth and milk, then add the remaining 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Bring the mixture to a boil, then reduce the heat to medium-low and simmer uncovered for 8 minutes, stirring occasionally.
Add the broccoli florets to the skillet, stir gently, and continue to simmer for another 5-7 minutes until the orzo is tender and the broccoli is bright green and tender-crisp.
Return the cooked chicken to the skillet and stir to combine.
Remove the skillet from heat and stir in the shredded cheddar cheese and paprika until the cheese is melted and the sauce is creamy.
Serve immediately.