Toss the dried apricots in a medium saucepan with the lemon zest, lemon juice, and water. Bring to a low boil over medium heat for about 10 to 15 minutes until the apricots are beginning to soften and plump up.
Reduce the heat to medium-low. Add the sugar and continue cooking until the sugar has completely dissolved, stirring occasionally, about 5 to 10 minutes.
Raise the heat back to medium and cook until the liquid has reduced by about half, and the color has deepened, about 10 to 15 minutes.
Let the apricots cool for about 10 minutes then using an immersion blender, purée the apricots until somewhat smooth in texture.
Stir in the vanilla bean paste.
Spoon into jars and keep refrigerated or process the jam in a water bath. Makes about 3 cups of jam.