Rinse apricots thoroughly, slice them in half, and remove the pits. Cut into quarters if needed.
Place the apricots, sugar (or fructose), water, lemon juice, and zest in a heavy-bottomed pot.
Bring to a boil, then reduce to low heat. Let it cook for 20 to 25 minutes (up to 2 hours for slow simmering) until the fruit breaks down and the mixture thickens.
Add a sprig of rosemary, basil, or a little fresh ginger near the end of cooking for extra flavor. Remove before jarring.
Pour the hot jam into sterilized jars, leaving 1 cm (ΒΌ inch) of headspace. Wipe rims clean, seal tightly, and turn jars upside down to cool and seal naturally.
Once fully cooled, turn jars upright and store in a cool, dark place. Refrigerate once opened and consume within two weeks.