Place the chopped apples in a large pot or slow cooker. Add the water, granulated sugar, brown sugar, ground cinnamon, ground ginger, ground cloves, salt, and lemon juice. Stir everything together to combine.
If using a stovetop, cook the apple mixture over medium heat, stirring occasionally, for 25 - 30 minutes. The apples should be soft and tender. If using a slow cooker, cook on low for 6-8 hours or on high for 3-4 hours, until the apples are soft and can be easily mashed with a fork.
Once the apples are soft and cooked down, you can choose to either use an immersion blender to blend the mixture until smooth, blend in a blender, or mash the apples with a potato masher for a chunkier texture.
If you prefer, you can stir in the vanilla extract at this point for added flavor. Taste the apple butter and adjust the sweetness by adding more sugar if needed, based on your preference.
Return the mixture to low heat and simmer for an additional 45 minutes to about an hour and a half, until it thickens to your desired consistency. Stir frequently to prevent sticking.
Transfer it to clean, airtight containers or glass jars. Store in the refrigerator.