Finishing should probably get its own SE site. :) I only partially jest.
In this case you will be up against several limitations to getting the finish that I think you are looking for, none of which should be considered insurmountable.
If you want to keep at it and try to get a nice even finish you will need to begin to flatten the actual varnish that is currently on the counter top taking care around the edges and corners not to sand through the finish. You need to physically cut the finish flat before considering adding more varnish on top of what is currently there because you are correct, future coats will only follow and magnify any contours that are present.
You have a couple of approaches to do this now with a varnish.
- Fine grit sandpaper and a sanding block.
Most of the time you don't actually need an actual block of wood to back up your sandpaper, sometimes you can get by with a stiff pad of some kind when sanding finishes such as lacquer. Varnishes are harder and stickier so you may want to opt for something pretty stiff to back up the sand paper.
A few more tips. Get a high quality 400 - 600 grit sticky back paper for finishing. 400 is about right. With the sticky back stuff, it comes in 4" or 4.5" rolls, you can get more creative and work faster when sanding finishes. You can wet sand it or dry sand it after a few days of curing. Wet is probably the way to go here. Be prepared to change to paper often. It will gum up and stop cutting then the temptation will be to just sand more vigorously which can lead to unevenness and sanding through.
I usually keep a sharp wedge of wood handy (picture a 5 degree incline plane 2 inches wide) to scrape the finish off of my sanding block / pad to get more milage out of the paper. The wood scraper does not damage the paper like a metal tool would and you can keep cutting at least twice as long per piece of paper.
Work in sections and dry the surface and evaluate your progress. You do want to evenly flatten the finish. I think you know what you are looking for, an even sheen indicating you have cut down the high points to the valleys.
If you completely sand though one coat into another you will sometime see ghost rings that can be seen under the correct light. These appear at the boundaries of coats of finish and are usually not something to worry about in a varnish finish as additional coats will cause these to be unnoticeable.
- Cabinet Scraper
A properly sharpened cabinet scraper can work miracles with a thick varnish finish. I add this just to tantalize you :). I have created mirror flat poly finishes with this tool and some good luck. I would consider this an advanced technique and would recommend practicing before I tried flattening a finish on an important project. However the time that a scraper can save you in sanding make it worth considering.
The key to this technique is to get a supremely fine and even burr on this guy and actually shave the finish with the lightest of pressure. On a well cured varnish, several days, you can almost produce little curls of finish. Care should be taken not to dig into the finish with the corners. (I usually round the corners on my cabinet scraper anyways for this very reason, not much mind you.)
Using a scraper has the disadvantage of being a more difficult technique but it can save hours if you get it right. The scraper will not gum up like paper and can produce a surface that is superior to all but the finest sandpaper. I would also only use a scraper with a varnish finish, the thicker finish the better.
Applying Final Coat
After you have satisfactorily flattened you finish, often done between coats of lacquer as well, you need to lay down the final coat or coats. The finish will need to flow properly but not be too thin and with a varnish, contamination is a big danger as these finishes take much longer to set up compared to a spray finish.
Applying the final coat of a varnish finish is probably beyond the scope of your question and I mainly wanted to highlight ways to flatten an existing coat varnish as this seems to be your most obvious next step. Best of luck Sir!