1. Preheat your oven to 350 F (175 C). Grease and flour an 8×8 inch square baking pan, or line it with parchment paper, leaving an overhang on two sides to easily lift the cake out later.

2. In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, packed light brown sugar, baking powder, baking soda, and salt. Ensure there are no lumps, especially in the brown sugar.

3. In a medium bowl, whisk together the sourdough discard, milk, melted butter, egg, and vanilla extract until well combined and smooth. The sourdough discard should be unfed and at room temperature for best mixing.

4. Pour the wet ingredients into the bowl with the dry ingredients. Stir gently with a spatula or wooden spoon until just combined. Be careful not to overmix; a few small lumps are fine.

5. Pour the cake batter evenly into your prepared 8×8 inch baking pan. Use the spatula to spread it into the corners and ensure the top is relatively smooth.

6. Place the pan in the preheated oven and bake for 25-30 minutes. The cake is done when a wooden skewer or toothpick inserted into the center comes out clean or with only a few moist crumbs attached. The top should be golden brown and spring back lightly when touched.

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