Depth here just means thinking more about their inner life and choosing a compliment based on your intimate knowledge about how they feel. That kind of compliment demonstrates the connection in a way that feels profound, rather than mere flattery.

About fifteen years ago I told my partner, rather artlessly I thought, that I love them not in spite of their flaws but because of them, too. It wasn’t what you’d call genius material but the words were intended to quell a deep fear of conditional love, and they still haven’t forgotten the compliment. Despite not being anywhere near poetry or a grand gesture, the fact that I realized this could not be left implicit was an important moment in our relationship.

Not a perfect example, but it’s the best I’ve got.