Preheat the oven to 350°F.
Butter eight cups in a twelve-cup muffin tin or line it with muffin liners.
butter for greasing or muffin liners
Brown the butter by melting and cooking it over a medium-low heat until it starts to leave brown bits at the bottom of the pan, swirling or stirring occasionally. This is right about when the bubbling sounds stop. Let cool slightly.
4 tablespoons (2 ounces) unsalted butter
Combine the dry ingredients (flour, sugar, baking powder, salt, cinnamon, and baking soda) in a medium-large bowl.
½ cup (57 grams) bleached all purpose flour, ¼ cup + 1 teaspoon (57grams) granulated sugar, ¾ teaspoon baking powder, ½ teaspoon salt, ½ teaspoon cinnamon, ¼ teaspoon baking soda
Combine the sourdough starter, buttermilk, egg, and vanilla in a small bowl. Add the cooled butter, and then add this mixture to the dry ingredients.
4 ounces (113 grams) 100% hydration sourdough discard, ¼ cup (2 ounces) buttermilk, shaken, 1 egg, slightly beaten, ½ teaspoon vanilla extract
Stir just enough to wet the dry ingredients, and then add the apple and mix to stir.
1 medium apple, cored, peeled, and chopped into ¼ inch cubes
Use a large cookie scoop or large spoon to fill the muffin cups about two-thirds of the way full.
Bake for about 18 minutes or until a toothpick inserted in the muffin comes out clean.
Cool in the pan for 5 to 10 minutes and then remove to a cooling rack to cool completely.
Store in an airtight container at room temperature.