Preheat the oven to 350F. Grease a standard 12-cup muffin pan with butter, and dust each muffin well with flour. Place ~½ tbsp brown sugar in the bottom of each muffin well. Set aside.
Prepare the apples. Mix together the apples and 2 tbsp of brown sugar in a medium bowl. Divide apples among the muffin wells by placing them in the bottom of each, on top of the brown sugar. Set aside.
Make the sourdough cake batter. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and apple pie spice. Set aside.
In a separate large mixing bowl, cream together the butter and both sugars.
Add the eggs, one at a time, beating well after each. Then, add the discard, greek yogurt, milk, and vanilla. Mix well.
Add the dry ingredients to the wet, and mix until just combined.
Divide the batter among the muffin wells, filling each ~⅔ full.
Bake at 350F for 15-20 mins, or until a toothpick inserted comes out clean.
Let the cakes cool in the pan for 5-10 mins while you make the warm butter soak.
In a medium saucepan over medium heat, combine all of the ingredients. Stir until the sugar is dissolved, then remove from heat.
Using a toothpick or fork, poke holes all over the cakes in the pan. Pour ~⅔ of the sauce all over the cakes, and let soak.
Carefully invert the cakes onto a serving plate.
Serve warm with vanilla ice cream and an extra drizzle of the warm butter soak.
