Cream Cheese & Chive Omelet. The first bite of creamy filling lets you know this isn't any old omelet. Make it once, and we suspect you'll be fixing it often. Jun 24, I love me some cheesecake, and will eat Philly Whipped Cream Cheese by the spoon (or container, whatever). But cream cheese in an omelet. The key to this healthy omelet recipe is cooking the eggs over low heat so the curds set up nice and soft. A splash of milk in the eggs is added insurance to keep.