Sour lacto-fermented dill pickles can be pretty close to polski ogorskis, depending on how long you leave them to ferment. Capretta covered it pretty much, but my recipe is:
8-10 cucumbers (pickling cukes when they're available from the markets, but lebanese will do also. The fresher the better).
4 cloves of garlic
8 peppercorns
1-2 tsp *dried* dill
some sort of tannic leaf (grape leaf, horseradish leaf, strawberry leaf)
5.4% brine solution (54g salt/1L water) - enough to cover pickles
Wash the cucumbers, chop 1cm off both ends and submerge the cukes in ice water for an hour. This ensures crunchy pickles, and is especially required if the cukes aren't freshly picked (i.e. are bought from the market). After removing from the ice water, pack the cukes into a wide mouth jar along with the garlic, peppercords, dill and tannic leaf. I use dried dill, as I find that fresh dill sometimes (depending on how old it is) can add a funky favour that isn't always welcome. Dried dill is easier to have on hand as well.
Pour the brine solution over the top of the cukes and ensure that the level of the brine is above the level of the cukes. I don't heat the water to dissolve the salt, the salt will dissolve if you stir the water enough. Cukes tend to float, so you'll need to weight them down with a heavy plate or a smaller glass jar that fits in the wide mouthed jar. Stick this in a cool dark cupboard somewhere. It's bound to bubble up and overflow, so sit the whole lot on a plate to catch anything that overflows. You want the temps to be as cool as possible (preferably 18-21C), so stick it in the fermentation fridge if you're happy that you won't get cross contamination. But higher temps will work, don't stress too much. Lacto is pretty forgiving.
Half sours take a few days to ferment out, and full sours around 1-2 weeks, depending on temperatures. You'll see the water go cloudy, which happens with lacto ferments and white powdery stuff collect at the bottom of the jar. All normal. If white mould forms on the top of the liquid, you can remove it. If you get mould of any other colour, probably best to discard and start again. I like really sour pickles, so I've leave them for up to a month, which can result in some funky mould growing on the surface (
pic here), but the pickles below are still delicious and crunchy.
Once they are sour enough for your liking, stick them in the fridge to slow down the fermentation process. I used to buy the large jars of polski ogorskis, but I actually prefer these pickles as they can be tailored to my preferences.
For anyone nervous about pathogens, measure the pH of your pickles during the ferment and you'll find that it drops pretty quickly. There's a quote somewhere from someone from the CDC saying that there have been no cases of botulism from home vegetable fermentation - most non-commercial food borne cases result from improper canning of low acid foods.