1. Preheat your oven to 375 F (190 C). Lightly grease and flour an 8×8 inch square baking pan or a 9-inch round cake pan.

2. In a large mixing bowl, combine the 1 1/2 cups all-purpose flour, 1/2 cup granulated sugar, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt. Whisk them together thoroughly until well combined.

3. In a separate medium bowl, whisk together the 1/2 cup melted butter, 1/2 cup sourdough discard, 1/2 cup milk, 1 large egg, and 1 teaspoon vanilla extract. Mix until everything is fully incorporated and smooth.

4. Pour the wet ingredient mixture into the dry ingredient mixture. Stir gently with a spatula or wooden spoon until just combined. Do not overmix.

5. For the crumb topping: In a small bowl, combine the 1/2 cup all-purpose flour, 1/4 cup packed light brown sugar, 1/4 cup granulated sugar, and 1/2 teaspoon ground cinnamon. Add the 1/4 cup cold butter, cut into small pieces. Use your fingertips or a pastry blender to cut the butter into the flour mixture until coarse crumbs form.

6. Pour the cake batter into your prepared baking pan and spread it evenly. Generously sprinkle the crumb topping over the entire surface of the batter. Place the pan in the preheated oven and bake for 30-35 minutes, or until a wooden skewer or toothpick inserted into the center of the cake comes out clean.

7. Once baked, remove the coffee cake from the oven and place it on a wire rack to cool for at least 15-20 minutes before slicing and serving.