Add the oil, butter, and onion to a pot over medium-high heat. Sauté the onion for 3-4 minutes.: You will smell the onion change from sharp to sweet as it softens, and you may hear a gentle sizzle when the onion hits the hot fat. Aim for translucence and slight softening rather than heavy browning, because this base will give the sauce a mellow sweetness. If the pan starts to brown too quickly, reduce the heat slightly to prevent bitter notes. A burnt onion flavor is the most common mistake here, so keep the heat controlled and stir occasionally.
Add in the broccoli and continue cooking for another 2 minutes, stirring often.: The broccoli will brighten in color as it heats and develop a tender edge while retaining some structure. You want the florets to soften slightly but not collapse, so cut them small for even cooking. The sound shifts from sizzle to a quieter simmer as moisture releases. If you prefer crisper broccoli, skip this quick cook and add it later in the process. Overcooking can make the broccoli soggy and dull the green flavor.
Stir in the garlic, Italian seasoning, and orzo, and cook for about 30 seconds.: The aroma will jump when the garlic hits the hot pan, scenting everything quickly, and the dry orzo will toast faintly, which deepens its flavor. This brief toasting helps the pasta maintain structure so it absorbs the liquid evenly. Be careful not to let the garlic brown, as it becomes bitter when overcooked; stirring constantly during this step avoids that common pitfall.
Add in the chicken broth, cream, and Worcestershire sauce. Once it just starts to boil, reduce the heat (to medium or even medium-low) and continue cooking for 10 minutes, uncovered, stirring fairly often. It should gently (but steadily) bubble vs. furiously boil, and you don't want the liquid to reduce too much before the pasta has cooked.: You will see tiny bubbles and steam rising as the liquid warms, and the smell becomes rich and savory from the broth and cream mingling. The orzo will begin to swell, soaking up the liquid and becoming tender. Stirring frequently prevents sticking and helps the starch release for a creamier sauce. If the heat is too high, the liquid will evaporate too quickly and the orzo may remain undercooked, so adjust the flame to maintain a gentle simmer.
Stir in the chicken.: When you fold the shredded chicken into the pot, you’ll notice the temperature settle and the dish turn heartier in texture. The chicken warms quickly and absorbs the surrounding flavors, which integrates the protein seamlessly. Give the pot a few gentle stirs so the pieces distribute evenly. A common error is adding cold chicken straight from the fridge which can cool the mixture and extend cooking time, so allow larger pieces to come closer to room temperature if possible.
Take the pot off the heat, stir in the cheddar until it's completely melted in, and season with salt & pepper (I am fairly generous with the salt). If needed, cover the pot and let it sit for a few minutes to let the sauce thicken.: The residual heat will melt the cheddar into a glossy, cohesive sauce, and you’ll see the mixture thicken as the cheese disperses. Stirring continuously will create a smooth finish and stop the cheese from clumping. Taste and adjust salt and pepper, because cheese and broth can vary in saltiness. If the sauce seems too thin, cover and let it rest a few minutes so the orzo absorbs more liquid; if too thick, add a splash of broth. Avoid high heat when melting the cheese or it may seize and become grainy.