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

Add the salted butter to a small saucepan over medium heat. Allow it to melt completely, then continue cooking, stirring or swirling the pan occasionally, as the butter begins to foam.

Keep cooking until the milk solids turn golden brown and the butter smells nutty and fragrant. Watch it closely during this stage, as the butter can go from perfectly browned to burnt quickly.

Once browned, immediately remove the butter from the heat and transfer it to a heatproof bowl. Allow it to cool slightly while you prepare the remaining components. The butter should still be liquid but should not be piping hot when added to the batter.

In a small bowl, combine the brown sugar, cinnamon, and flour. Stir until evenly combined, then set aside.

The small amount of flour helps keep the cinnamon-sugar layer from melting completely into the cake as it bakes.

In another bowl, combine the melted butter, brown sugar, and flour.

Stir with a fork until the mixture forms coarse, crumbly pieces. Set aside while you prepare the cake batter.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg.

Whisk thoroughly so the leavening agents and spices are evenly distributed throughout the flour. Set aside.

In a large mixing bowl, whisk together the slightly cooled brown butter, granulated sugar, and brown sugar until well combined.

Add the eggs and whisk until smooth. Then add the Greek yogurt, pumpkin puree, sourdough discard, and vanilla extract. Whisk until the mixture is smooth and evenly combined.

The ingredients being at room temperature will help the batter come together more easily and prevent the browned butter from firming up when mixed with the other ingredients.

Add the dry ingredients to the wet ingredients.

Using a spatula or wooden spoon, gently fold until just combined. Be careful not to overmix the batter. A few small streaks of flour are fine, but continue folding gently until no dry flour remains.

The batter will be fairly thick.

Spread half of the batter evenly into the prepared 9-inch springform pan.

Sprinkle the cinnamon-sugar mixture evenly over the surface of the batter, keeping it away from the very edge of the pan if possible.

Carefully spoon the remaining batter over the cinnamon layer and gently spread it into an even layer. Take care not to disturb the cinnamon swirl underneath.

Sprinkle the crumble topping evenly over the top of the cake.

Bake at 350°F (175°C) for about 55 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean or with a few moist crumbs.

Because ovens and pans can vary, begin checking the cake around the 50-minute mark. If the top is browning too quickly before the center is finished, loosely tent the cake with foil for the remainder of the baking time.

Allow the coffee cake to cool in the springform pan before removing the sides.

For the cleanest slices and the best texture, allow the cake to cool completely before adding the icing.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.

If the icing is too thick to drizzle, add a few drops of milk at a time until it reaches your desired consistency. If it becomes too thin, whisk in a little more powdered sugar.

Drizzle the icing generously over the cooled coffee cake.

Slice and serve!