Prepare the meatball mixture: In a large bowl, combine ground chicken, beaten egg, grated parmesan cheese, chopped parsley, kosher salt, black pepper, whole milk, breadcrumbs, minced garlic, and chopped yellow onion. Mix gently but thoroughly until all ingredients are well incorporated, being careful not to overmix as this can make the meatballs tough.
Form and brown the meatballs: With lightly greased hands to prevent sticking, form the mixture into 16 evenly sized meatballs (about 1½ inches in diameter). Heat olive oil in a large skillet over medium heat. Add the meatballs, working in batches if necessary to avoid overcrowding, and brown on all sides until the internal temperature reaches 165°F, approximately 8-10 minutes. Transfer to a plate and cover loosely with foil to keep warm.
Start the pasta base: In the same skillet, melt the butter over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Add the minced garlic and cook for another 30 seconds until fragrant. Pour in the chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan to incorporate those flavors into the sauce.
Create the creamy sauce: Add the softened sun-dried tomatoes, cream cheese, salt, and pepper to the skillet. Stir until the cream cheese has completely melted and the mixture is smooth. This forms the flavorful base of your creamy sauce.
Cook the orzo: Add the orzo pasta and heavy whipping cream to the skillet and bring the mixture to a gentle simmer. Cover the skillet and reduce heat to medium-low. Cook for 12-15 minutes, stirring occasionally to prevent sticking, until the orzo is tender. During the last 5 minutes of cooking, stir in the parmesan, cheddar, and Monterey Jack cheeses until melted and the sauce is creamy and smooth.
Combine and finish the dish: Return the meatballs to the skillet, nestling them into the creamy orzo. Simmer uncovered for 2-3 minutes until the meatballs are heated through. Remove from heat and let the dish rest for 5 minutes to allow the sauce to thicken slightly. Garnish with chopped fresh parsley and additional sun-dried tomatoes before serving.