Season the chicken with salt, pepper, and paprika. Toss to coat evenly.
Warm the olive oil and butter in a large deep skillet over medium-high heat.
Sear the chicken in two batches until lightly browned, 3–4 minutes per side. Transfer to a plate.
Soften the onion in the same skillet over medium heat, 2–3 minutes, scraping up brown bits.
Stir in the garlic, Italian seasoning, and red pepper flakes. Cook until fragrant, about 30 seconds.
Add the sun-dried tomatoes and orzo. Toast, stirring, for 1 minute.
Pour in the chicken broth and heavy cream. Bring to a gentle simmer.
Simmer uncovered, stirring often, until the orzo is just tender, 9–11 minutes.
Return the chicken and any juices to the pan. Simmer until the chicken is cooked through, 2–3 minutes.
Fold in Parmesan and basil. Add lemon juice if using. Adjust salt and pepper to taste.
Let stand 2 minutes to thicken, then serve hot with extra Parmesan.