Preheat your oven to 350°F (168°C) and lightly grease a 9" x 5" loaf pan and line with parchment paper. This cake batter can be made with a stand mixer or an electric hand mixer. Make sure the cold ingregients have come to room temperature before starting.
To the bowl of a stand mixer, add 2 sticks unsalted butter and 1 ½ cups granulated sugar and beat until the mixture is fluffy and light in color.
Add 4 large eggs, one at a time, waiting until each is fully incorporated before adding the next one. Add ¼ cup milk, 1 teaspoon vanilla extract, and ½ cup sourdough discard and mix until smooth.
Next, add 2 cups all-purpose flour and 1 teaspoon salt and mix on low speed until the mixture is smooth.
Pour the mixture into the loaf pan and bake for 60-70 minutes or until a toothpick inserted in the center of the cake comes out clean.
Remove the cake from the oven and allow it to cool in the loaf pan for 10-15 minutes before transferring it to a cooling rack.