Pat chicken dry and cut into 1-inch pieces. Toss with 1 tablespoon olive oil, 1 tablespoon Cajun seasoning, salt, and pepper until evenly coated.
Heat remaining 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Sear chicken pieces without overcrowding, about 3-4 minutes per side, until golden brown. Work in batches if needed. Remove chicken and set aside.
Reduce heat to medium. Add butter to the pot and melt, scraping up browned bits. Sauté diced onion and red bell pepper for 5-7 minutes until softened and translucent.
Add minced garlic, dried oregano, thyme, and smoked paprika if using. Cook, stirring constantly, for 1 minute until fragrant.
Stir in uncooked orzo pasta and toast lightly for about 30 seconds to 1 minute.
Pour in chicken broth, stirring well and scraping up any remaining browned bits. Bring to a gentle simmer.
Reduce heat to low, cover, and cook orzo for 10-12 minutes, stirring occasionally, until liquid is mostly absorbed and orzo is tender but firm.
Remove pot from heat. Stir in heavy cream until well combined and creamy.
Gradually add grated Parmesan cheese, stirring until melted and sauce is smooth and velvety.
Return seared chicken to the pot and gently fold it into the orzo Alfredo mixture to warm through.
Serve immediately, garnished with chopped fresh parsley and extra Parmesan if desired.