Put apple juice, lemon juice, sugar, and cinnamon sticks in a large, heavy bottomed saucepan. I LOVE using my Dutch Oven for this.

Peel, core, and cut apples into 1/2-inch thick slices. (See Notes below.); Work with one apple at a time and add to the pot, stirring to coat with lemon juice mixture so they don't turn brown.

Bring to a boil over medium heat; cover with a lid and reduce to a simmer.

Cook for about 30 minutes over low heat, stirring often, until apples are fork tender. (A fork should slide into them easily, but they shouldn't be mushy.)

Remove cinnamon sticks and discard.

Mash with a potato masher, and stir in the 1/4 - 1/2 teaspoon ground cinnamon and dash of nutmeg.

If required, add more sugar to taste.

Delicious warm, room temperature or cold!