Brown the butter. Melt the salted butter in a saucepan over medium heat. Cook, stirring or swirling frequently, until the butter foams, develops a nutty aroma, and forms golden-brown specks. Immediately transfer it to a heatproof bowl and let it cool until warm but not hot.

Make the crumble. Combine the melted butter, brown sugar, and flour in a small bowl. Mix with a fork until small clumps form. Set aside.

Prepare the oven and pan. Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment paper.

Combine the dry ingredients. Reserve 2 teaspoons of the measured flour. Whisk the remaining flour with the baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.

Prepare the apples. Peel and chop the apples into small pieces. Toss with the reserved 2 teaspoons of flour.

Mix the wet ingredients. Whisk the browned butter and granulated sugar together. Add the eggs one at a time, whisking after each addition. Mix in the Greek yogurt, sourdough discard, and vanilla extract.

Finish the batter. Gently fold the dry ingredients into the wet mixture until just combined. Fold in the prepared apples.

Add the crumble. Spread the batter evenly into the prepared springform pan. Sprinkle the brown sugar crumble over the top.

Bake. Bake for 55–60 minutes, beginning to check around 50 minutes. The top should be golden, and a toothpick inserted into the cake portion should come out clean or with a few moist crumbs. Cover loosely with foil if the topping browns too quickly.

Cool. Let the cake cool in the pan for 15–20 minutes before releasing the springform ring. Allow it to cool further before glazing.

Make the glaze. Whisk the powdered sugar, milk, maple extract, and vanilla extract until smooth. Adjust the consistency with a few drops of milk or a little more powdered sugar as needed.

Glaze and serve. Drizzle the glaze over the cooled cake. Let it set briefly, slice, and serve.