If you soak your beans in brine (3tbsp table salt per gallon of water, or 1.5% salt by weight) it'll help soften the skins by replacing calcium and magnesium ions in the skin. After soaking for 8–24 hours, drain and rinse. (Source: Cooks Illustrated, login required). Harold McGee in On Food and Cooking also mentions this (p. 488–489) and suggests 1% salt by weight. McGee also mentions that 0.5% baking soda will further reduce cooking times (but may lead to unpleasant taste & mouth feel).
Alternatively, Cook's Illustrated also reports that dried kombu can be used to similar effect, without needing the soak.
Even after brining, taste them when nearly done cooking: you may need to add some salt—it doesn't always penetrate that far into the beans. At least, that's been my experience.
Quick summary:
- Create 1–1.5% salt (by weight) brine, approx 3tbsp table salt per gallon of water.
- Sort (remove rocks, deformed and damaged beans, etc.) and rinse dried beans. Drain rinse water.
- Soak rinsed beans in brine for 8–24 hours. Beans will noticeably swell.
- Drain brine, rinse beans again.
- Cook beans normally. Towards the end of cooking, season to taste.
You want to season towards the end of the cooking because it results in creamier texture and also eating some beans which haven't been heated to boiling for 10 minutes is ill-advised due to phytohaemagglutinin.
You don't need to add any water to the slow cooker whatsoever. Your recipe is somewhat similar to the one that I use to cook my lunches but the quantities seem larger than mine, much larger. I assume that you chop everything up into small piece, including the chicken. The slow cooker should not be more than 3/4 full, so reduce your amounts if the quantities are too big.
Chicken breast doesn't need more than three hours on the 'high' setting in order to cook (six hours on low); this cooking time leaves most of the vegetables crisp (courgettes and pumpkin soften, but bell peppers, carrots and onions retain their texture).
Running a kosher kitchen, I would not know about adding cheese to the food, but anyway I would recommend adding the cheese to the food prior to serving, not while it is being cooked.
If you wish to separate some of the vegetables, one technique which I have used successfully is to put these vegetables in a wire tray (I use the plastic punnets in which we buy fresh mushrooms): these vegetable are cooked like the rest but are kept separate.
If you do wish to add certain vegetables after you have already started cooking, then you are supposed to add 20 minutes to the cooking time (every time one opens the lid of the cooker, steam escapes and it apparently takes 20 minutes to obtain the same amount of steam).
Best Answer
If you live in Poland, you should easily find the "normal" white ones in your supermarket. They should be good for baked beans, although the British version uses white beans that are a bit smaller.
For more American style beans, you could also use the pinkish-brown or spotted type.
There are so many types of beans, that I can't give a specific "name". Stick with the smaller ones, as they have less starchy parts and usually keep their shape better.