Heat a large skillet or deep sauté pan over medium heat. Add the butter and olive oil. Once the butter is melted, add the minced garlic and cook for about 1 minute while stirring often until fragrant and softened.
Add the dry orzo pasta directly into the skillet. Stir continuously for 2 to 3 minutes so the pasta lightly toasts in the garlic butter mixture. Some pieces may become lightly golden.
Slowly pour in the chicken broth and whole milk while stirring to combine. Add the salt, black pepper, and Italian seasoning. Stir well so the seasonings evenly distribute throughout the liquid.
Bring the mixture to a gentle boil over medium heat. Once bubbling, lower the heat to medium-low and simmer uncovered for 10 to 12 minutes. Stir often to keep the orzo from sticking to the bottom of the pan.
Continue cooking until the orzo becomes soft and creamy and most of the liquid is absorbed. If the mixture becomes too thick before the pasta finishes cooking, stir in a splash of extra broth or milk.
Turn off the heat and slowly stir in the freshly grated parmesan cheese. Mix continuously until the cheese fully melts into the sauce and becomes smooth and creamy.
Taste the orzo and adjust the salt and pepper if needed. Sprinkle chopped fresh parsley over the top before serving.
Serve warm while the sauce is creamy and smooth.