Preheat oven to 350 F then coat your doughnut pan with cooking spray.
How to brown butter: melt butter over medium heat in a small light-bottom saucepan so you can keep track of the color. Swirl the pan occasionally to make sure that the butter is cooking evenly. As the butter melts, it will begin to foam and change color from yellow to golden to light brown. Once the butter turns light brown and you smell a nutty aroma (about 5 minutes), remove the butter from heat and pour into a bowl. Side note: you will start to see little brown specks on the bottom of the pan when the butter is cooking. Those are the milk solids, which cook faster and settle on the bottom of the pan. They have a slightly burnt taste (which I love) so when using your brown butter, it’s up to you if you want to use this sediment in your recipe. I did!
Whisk together egg, almond milk, vanilla extract and brown butter in a small bowl.
Combine flour, baking powder, baking soda, salt, ground cinnamon, ground nutmeg, ground ginger and brown sugar in a medium bowl. Mix until well combined.
Stir wet ingredients from step 3 into the dry ingredients from step 4. Mix until well combined then stir in minced apple. Stir the mixture until all ingredients are evenly distributed but try not to over mix the batter.
Pour batter into a piping bag then pipe the batter into each doughnut mold about 3/4 the way full. Bake the doughnuts for about 8-10 minutes or until golden. If you don’t have a piping bag, you can always use a large Ziploc bag and cut off the corner or spoon the batter into the doughnut pan.
Allow the doughnuts to cool on a wire rack. Make the maple spiced rum brown butter glaze while doughnuts cool.