Combine apples, cider (or water), and lemon juice in a heavy pot. Bring to a simmer, then reduce heat to a gentle bubble. Cover and cook, stirring occasionally, until the apples are completely soft (20–30 minutes).
Mash the apples with a potato masher or blend briefly for a smoother texture. If you like it chunky, keep some texture; if you prefer velvet smooth, go for a quick puree.
Stir in sugar, cinnamon, cloves (if using), and a pinch of salt. Simmer uncovered, stirring often to prevent sticking, until the mixture thickens to a jammy, spoonable consistency (about 30–40 minutes).
Skim off any foam, then test the texture on a chilled plate. If it runs slowly, you’re in the right zone. If it’s still too watery, cook a bit longer and stir more frequently.
Remove from heat and cool slightly. Transfer to clean jars or a container. Refrigerate up to 2–3 weeks or process in a water bath for longer shelf life.