1.
Sterilize jars and lids: boil for 10 minutes in a large pot of hot water. Lift jars and lids out not with your hands but with tongs and place them on a spread dish towel.
2.
Scrub oranges with a vegetable brush under running warm water. Cut off one end of the fruits. Make lengthwise cuts into quarters so that the quarters are still held together at the intact end of the orange. Cut over a bowl to catch the juice. Gently open the oranges, sprinkle the salt (except for 1 TBSP) on the cut surfaces and press the fruit firmly back together.
3.
Place the fruits close together in a sterilized preserving jar (with an acid-resistant lid). Halve the additional orange, squeeze it, and add the juice along with the previously collected juice and the remaining salt into the jar. If there is still some space in the jar, weigh down the oranges with a sterilized pebble or small jar lid (Weck) of suitable size and fill the jar with boiling water so the oranges are completely covered. Close the jar with the lid. For the first 10 days, alternate placing the jars on the lid and then on the jar bottom each day. Then let rest in a dark, not too warm place (e.g., cellar) for at least 3 to 4 weeks (or longer).
4.
The oranges remain shelf-stable in the closed jar for about one year. Remove oranges with a clean fork each time to avoid introducing bacteria into the jar. Store in the refrigerator after opening.