Add the chopped apples, apple cider, brown sugar, maple syrup, cinnamon sticks, and orange peel to a medium heavy-bottomed saucepan or Dutch oven.
Bring to a gentle simmer over medium heat. Reduce the heat to medium-low, cover, and cook for 30–40 minutes, stirring occasionally, until the apples are extremely soft and beginning to fall apart.
Remove and discard the cinnamon sticks and orange peel. Using an immersion blender, blend the apples directly in the pot until completely smooth. You can also carefully transfer the mixture to a blender.
Stir in the ground cinnamon, ginger, nutmeg, cloves, kosher salt, and lemon juice.
Return to low heat and cook uncovered for 1–2 hours, stirring more frequently as the apple butter thickens. You’re looking for a deep caramel-brown color and a thick, glossy consistency that holds its shape on a spoon. The longer you let it slowly reduce, the richer the flavor will become.
Remove from the heat and stir in the vanilla extract. Taste and adjust with another pinch of salt or squeeze of lemon, if needed.
Let cool completely before transferring to a jar. The apple butter will continue to thicken as it cools.