Wash the stone fruits. Remove the pits and cut them into small pieces.
Put in a saucepan with ¾ cup of sugar (and lemon juice if making peach jam). Bring to a boil (bubbling evenly throughout, not just the edges) then simmer uncovered for 10 minutes.
Stir frequently to prevent burning. Let it cool completely to room temperature. Repeat this process a second time.
For extra smooth filling, use an immersion blender after the first or second boiling.
Boil, completely cool and re-boil the jam again. Let it cool completely. The jam will thicken naturally without pectin or other thickeners.
Notes
This process takes a long time so be prepared to do this step at least a day before you need the filling.