Heat olive oil and butter in a large skillet over medium-high heat.
Season chicken cubes with salt, pepper, and oregano, then add to the skillet and sear until browned and cooked through (5-7 minutes).
Remove chicken from the skillet and set aside on a plate.
Add minced garlic and sun-dried tomatoes to the skillet and sauté for 1 minute until fragrant.
Add dry orzo to the skillet and toast for 2 minutes, stirring frequently to prevent burning.
Pour in chicken broth and bring to a gentle boil.
Reduce heat to medium-low, cover, and simmer for 10-12 minutes or until the orzo is tender and most of the liquid is absorbed.
Stir in heavy cream, Parmesan cheese, and baby spinach until the spinach has wilted and the sauce is thickened.
Return the cooked chicken to the skillet and stir to combine.
Garnish with fresh parsley and serve immediately.