Cut the apricots in half (or in quarters if they’re on the larger side) and discard the pits. You can leave the skin on; it will break down when the apricots are cooked.
In a large, heavy pot over medium-high heat, combine the apricots, orange juice and 1/3 cup sugar and stir. Once the mixture is warmed through and the juices start to release, add the salt and turn the heat up to medium-high. Continue to cook, stirring frequently with a wooden spoon, until the fruit breaks down and resembles a puree, about 15 minutes. Taste for sweetness and add more sugar, if necessary. When the jam reads 190F to 200F on a candy thermometer, remove the jam from the heat and transfer to a bowl to stop the cooking process. Give it a few more stirs to release the steam and allow it to cool completely. Use at once of transfer the jam to a clean glass jar and keep it in the fridge for up to 2 weeks.