Three things that might help:
Shared vulnerability. I’d say this is what you mean with “deep”. Others said it well, if you force it then it’s awkward.
Which brings me to the second thing: progressive self-disclosure. In other words, with each person you meet there’s a set of steps in a staircase. You meet everyone in level one. If you open up a bit and they walk up with you, you can continue going up a bit more and see if they go up with you a bit more. You need to notice where others are: are they visibly comfortable? Are they being enthusiastic about the topic?
The final thing is shared competence. Sometimes, talking “deep” is finding someone who knows the same stuff that you know about and you go on a wild ride, exploring your mental palaces and building new ones throughout the conversation. This also requires going up step by step.
If you’re kind and lucky, you will find people with whom you can have shared vulnerability and people with whom you can have shared competence.
Check out these resources that might help:
- Popular by Mitch Prinstein
- Crucial Conversations

For one, it would help to stop saying that phrase.
Better to call the opposite: