While a long, persistent, unblinking gaze may not seem like a friendly gesture to a human, eye contact is another way how cats show affection. Cats only make eye contact with people they like, and they even make eye kisses. This behavior is when a cat will gaze with its eyelids half-closed and blink slowly, repeatedly.
You can return this gesture. If you see your cat giving eye kisses, you may want to give her one kiss in return.