Start by heating the olive oil and butter in a large pan over medium heat. You will know it is ready when the oil shimmers and the butter foams. Add the chicken breasts and cook until they are golden and cooked through, about 6-8 minutes per side. Avoid overcrowding the pan to ensure even cooking.
Once the chicken is cooked, toss in the minced garlic and Italian seasoning. Stir it around until the garlic smells fragrant, which should take about a minute. Do not let it brown too much, or it can turn bitter.
Mix in the diced sun-dried tomatoes and let them soften for another couple of minutes. If they stick to the pan, add a splash of milk to loosen things up.
Pour in the heavy cream and the rest of the milk, stirring gently. Keep an eye on it as it thickens, stirring continuously for about 3 to 5 minutes to avoid lumps.
Add the baby spinach, folding it into the sauce until it is wilted and bright, about 2-3 minutes.
After cooking the penne or macaroni separately, toss it into the creamy mixture. Ensure every noodle is coated. If the sauce seems too thick, add a splash of milk or some pasta water to loosen it.
Finally, sprinkle in the grated Parmesan cheese, stirring until it melts into the sauce. Taste and adjust seasoning with salt and pepper as needed.