Add the oil, butter, and onion to a pot over medium-high heat. Sauté the onion for 3-4 minutes.: As the pot heats, you will hear a gentle sizzle when the olive oil and butter meet the pan, and the aroma of the onion will shift from sharp to sweet within a few minutes. Visually, the onion should turn translucent and glossy, not browned; that translucence signals that the sugars are releasing and building a mellow base. Work with moderate heat so the fat does not brown too quickly, and stir occasionally to keep the pieces moving. A common mistake is cooking too hot which causes rapid browning, leading to a bitter undertone instead of gentle sweetness.
Add the garlic, Italian seasoning, and orzo. Cook for 2-3 minutes, stirring often.: The moment you add the garlic and Italian seasoning , the kitchen fills with a warm, herbaceous scent. Toss in the orzo and let it toast lightly; you will notice the grains take on a slight sheen and the scent deepens into nutty notes. Stirring often prevents sticking and ensures the orzo toasts evenly, which adds a subtle depth when it later absorbs the broth. Avoid walking away at this stage, because garlic can turn bitter if it browns too much. If you see dark flecks, reduce the heat and start over with fresh aromatics.
Stir in the chicken broth, cream, pesto, sun-dried tomatoes, and asparagus. Once it starts to bubble, continue cooking for 10 minutes, uncovered, stirring fairly often. You will likely need to turn the heat down a bit (to medium or even medium-low). You want it to gently bubble vs. furiously boil, and you don't want the liquid to reduce too much before the pasta has cooked.: When the liquids hit the pan, they will hiss and release steam, and you should bring them to a gentle simmer so the orzo can absorb evenly. The combination of chicken broth and cream creates a milky swirl as it heats, and the pesto will streak the surface with green ribbons before folding in. Keep stirring fairly often to prevent the orzo from settling and clumping at the bottom, and watch how the sauce thickens; it should coat a spoon without becoming gluey. Turn the heat down if the bubbling becomes aggressive, because a furious boil will evaporate liquid too quickly, leaving undercooked pasta. If you notice the liquid disappearing before the orzo is tender, add a splash more chicken broth to maintain the right cooking environment. A pitfall here is not adjusting the heat, which can either over reduce the sauce or leave the pasta undercooked.
Stir in the cooked chicken (let it warm through for a minute or so).: Adding pre cooked chicken at this stage lets it heat gently without drying out. You will feel the temperature of the pot change and see the chicken pieces steam slightly as they warm. The meat absorbs some of the sauce, which integrates flavors and makes the dish more cohesive. Stirring ensures each shred gets a touch of sauce, but resist the urge to cook it vigorously; extended high heat will toughen the protein. A typical error is overheating the meat which causes it to lose moisture and become stringy.
Take the pot off the heat and stir in the parmesan cheese. Give it a taste, and if the pasta is firmer than you'd like or you want the sauce to be thicker/more absorbed, cover the pot and let it sit for a few minutes. If the sauce has reduced too much, add in a splash of cream. Season with salt & pepper as needed and enjoy immediately.: Off the heat, stirring in parmesan cheese creates a glossy finish as the cheese melts into the warm sauce, adding savory brightness and slight thickness. Taste now to assess seasoning and texture; the short rest under a lid allows the residual heat to finish cooking the orzo and helps the sauce cling more tightly. If the mixture seems too wet, a brief uncovered rest will let the orzo absorb excess liquid. Conversely, if the sauce is overly reduced, add a splash of extra cream or chicken broth and stir to reincorporate. Over seasoning at this point can make the dish too salty because of the parmesan cheese and chicken broth , so add salt and pepper sparingly and taste between adjustments. A common misstep is skipping the rest period which can leave the pasta underdone or the sauce too loose.