1-Prepare the apples: by removing the cores and cutting them into large chunks or wedges (peel if desired).

2-Combine the apples, cinnamon stick (or ground cinnamon), lemon juice (or substitute), vanilla extract, and star anise (if using): in a large heavy pot.

3-Add 1/4 cup water and stir to mix, then cover the pot and cook over medium-low heat, stirring occasionally, until the apples are very soft, about 25 to 35 minutes.

4-If the pot becomes dry, add more water as needed, then remove from heat and let cool slightly.

5-Taste and add sweetener if desired, starting with a small amount, then mash or blend the apples to your preferred consistency, either with a food mill to remove skins or by blending with skins on.

6-If the mixture is too watery, simmer gently to thicken.