Add all ingredients to a medium saucepan on medium-high heat. Give it a stir. Bring it to a boil, and then reduce the heat to medium-low. Cover it with the lid slightly ajar. Let it simmer for 20 minutes, giving it a stir every 5-10 minutes or so, just to prevent it from burning on the bottom. 

After about 20 minutes, the apricots should be very soft. Using a potato masher or whatever works for you, mash the apricots down if you do not want whole apricot pieces in your sauce. Give it a taste and adjust seasonings as needed (or add more sugar or vinegar to adjust taste). Cover again, with the lid slightly ajar, and continue simmering the sauce for another 20 minutes or so, again stirring every 5-10 minutes.

If the sauce looks thick enough for your tastes, remove it from the heat and let it cool for at least 20 minutes prior to transferring it to airtight jars. The sauce should keep for about a week in the fridge.