Begin by peeling, coring, and roughly chopping the apples. This will make them easier to cook down into a smooth consistency.
In a large pot or Dutch oven, combine the prepared apples, granulated white sugar, brown sugar, cinnamon sticks (or ground cinnamon), ground cloves, ground nutmeg, water, and cider vinegar.
Place the pot over medium heat. Allow the mixture to cook until the apples become soft and can be easily mashed, approximately 30 to 40 minutes. Stir occasionally to prevent sticking.
Once the apples are soft, use a wooden spoon or potato masher to mash the apples into a sauce-like consistency. For a smoother apple butter, you can use an immersion blender or transfer the mixture to a regular blender and blend until smooth.
Reduce the heat to low and let the mixture simmer. Continue to cook, stirring occasionally, for 1.5 to 2 hours, or until the apple butter reaches your desired thickness.
Taste the apple butter and adjust the seasoning, adding more sugar or spices if necessary according to your preference.
Once the apple butter has reached the desired consistency, remove the pot from the heat. If you used cinnamon sticks, remove them at this point. Allow the apple butter to cool to room temperature. It will continue to thicken as it cools.
Optional: If you want to store the apple butter for an extended period, you can can it in sterilized jars. Alternatively, it can be stored in an airtight container in the refrigerator for up to two weeks.
Your homemade apple butter is now ready to be enjoyed! Use it as a spread on toast, a filling for pastries, or as a flavorful addition to various recipes.