Cover the base of a 6 litre pot with oil and place over medium–low heat. Add the speck and fry for about 5 minutes. Add the onion, reduce the heat to low and sweat until translucent, stirring regularly, about 5 minutes. Add the potato, cook briefly, then increase the heat to high and deglaze the pot with the stock. Put a lid on the pot, bring to a simmer, reduce the heat to low and cook for about 20 minutes.
Add the beans, summer savoury and pepper. Season to taste with the salt flakes. Add the speck skin, then stir and bring to a simmer. Cook on low heat for 30 minutes, covered. When the potato is soft, turn the heat off and use a potato masher to carefully mash the potato just a little – maybe 15 times – so you have some mashed and some chunks. This also thickens the soup.
Let the soup cool for 15 minutes, then remove and discard the speck skin.
Taste the soup. Now start to season by adding a little of the vinegar, sugar, pepper and salt. You are looking for a punchy broth that is sweet, sour and salty. Add more vinegar, sugar, pepper or salt, as needed.