How to submit two separate works simultaneously to two conferences when the works are similar in a few parts?
I had done something similar during my PhD (upon advice by my supervisors). I'll explain my situation as it seems similar to yours (though you only told us about the similarities but not the differences between the content you have for your two papers).

I've developed a novel technique as well, and had quite a bit of results, though not quite enough for a journal submission. We submitted two conference papers:


The first one was targeting a smaller, very specialized conference, specifically in the subfield focused on the theory used in my technique; here we submitted a paper dissecting the theory behind my new technique and offering an exhaustive test of parameters and similar.
The second one in a much wider-topic conference, focusing on the performance of the method on the datasets of wide interest and comparison to other state of the art.


The theory was discussed at length in the theoretical paper. However, as there was no guarantee either of the papers would be published, we also introduced the theory in the other paper in a much denser and shorter, but still complete (i.e. containing everything necessary to make my experiments repeatable) manner. We then referred to the theory paper in the performance paper.

For cross-citation of such papers:


upload them both to preprint services (arXiv is fine but occasionally there is institutional services which are much less demanding to use)
cite them as (submitted) or (submitted to X) or (under review) and update it through the submission process (if you pass the first round of reviews)
some conferences allow/require to send a copy of any relevant but unpublished materials, so you can also send the second manuscript as supporting material with the submission (especially if, for any reason, you did not manage to use a pre-print service).
make sure there is no "significant overlap" between the papers (which would constitute auto-plagiarism) and that you are not re-using your own text


Most importantly though, if you can, talk to your supervisor. They will likely have experience and will be able to advise you best since they know your work.