One suggestion might be to use more concrete examples, to give the reader tangible evidence of your ideas. You can use this method in a number of ways.
One would be to take an essay (or other piece) you are unsatisfied with and highlight the parts that you feel are too "wanting-to-be-deep", which I imagine (could be wrong here) to be a too-cerebral or "generalized" approach. For each of these parts, imagine some situation or analogy (from life itself) that illustrates what you mean. These would be separate, possibly unrelated examples of your ideas. Then see if you find a thread between the narratives/ examples that ties any of them together, or select one or two you prefer and see if you can use it/them to connect your abstract thoughts into a more tangible and coherent whole.
This sounds more convoluted than it really is! I find this to be a sort of focused brainstorming revision process, and hopefully can help to get your mind connecting less rhetorical and more substantive dots.
Another approach could be to scrap the previous draft and consider your idea from the ground up. Think first about the point you are trying to make. But remember to allow your writing to carry you beyond your preconceived notion about what it will be; use your objective as a starting rather than a finishing point. The best writing always surprises the author on some level. So then imagine that original "point" you're working on in various scenarios or applications. If what you come up with seems too "pedestrian", try to think of something that has emotional as well as cerebral content. Even mathematical concepts can form stories, so try to make connections.
Also consider visual or other sensuous illustration. Then, play with it. Try moving parts around. 487
Or try asking questions instead of only declarative/ explanatory sentences. At some point something should "click."
Finally, think of clichés associated with your idea. See if you can twist or turn them around or make them unexpectedly surreal or different. People often think in clichés without realizing it. When you turn it around, this wakes the reader up, either by being true in an unexpected way or by creating a sense of renewal about the mundane. That's a cheap trick, yes, but oddly it seems to work more than you might think. Of course, here I am not giving you concrete examples...but I'm not sure about the type of essay you're thinking about. Cliché could be common phrases, familiar fables or fairy tales, pop culture references, or something entirely different.
Remember to avoid dull and expected generalization. All ideas are better presented using examples, metaphors or visual references, etc, something like a virtual power point. Also choose one basic thread or a few examples that can tie together from the examples you came up with. Then if you want to generalize at the end, see if you can find some kind of transformation or "turning point", appropriate to your subject. You only have to hint at it, if that's your style. Or be more forceful if that feels right. 487