Preheat the oven to 350°F and grease a 9-inch round cake pan with cake goop or line with parchment paper. Scrunching the parchment into a ball and, running it under water, and drying it with a paper towel will make parchment soft and easier to shape; line so that some parchment comes up over the sides of the pan. Use the parchment to lift it out of the pan after baking. Spraying the pan with nonstick spray before adding the parchment can help secure it in place while you add the batter. Peel the 4 large Granny Smith appleschop them into cubes, and set aside. If you were to slice off half the apple beyond the core, you'd cut that half into 9 pieces (3x3 pieces about ¾ to 1 sq. inch). Then, use that same ratio to chop the rest of the apple.
Add 3 cups all-purpose flour, ¾ cup light brown sugar, 2 teaspoons baking powder, 2 teaspoons ground cinnamon, 1 teaspoon sea salt, ½ teaspoon ground cardamom, and ¼ teaspoon ground nutmeg into a stand mixer bowl fitted with a whisk attachment.
Add ¾ cup salted butter (make sure it's very soft but not melted) into the dry ingredients and mix until the mixture has a sandy appearance; this is called reverse creaming.
Switch to a paddle attachment on the mixer. Add the chopped apples to the flour and butter mixture and mix at low speed to coat them thoroughly.
In a separate bowl, beat together 2 large eggs and ¾ cup whole milk together. Add this mixture to the apples and flour along with 2 teaspoons vanilla bean paste and mix at low speed until just combined. The batter will be thick.
Transfer the batter to the prepared cake pan and use a rubber spatula to spread the top evenly.
Sprinkle 2 tablespoons granulated sugar over the top of the cake batter before baking.
Bake for 50 to 65 minutes or until the center of the cake reaches 200°F. The top of the cake should be golden brown and have a harder, cracked crust.
Remove the cake from the oven and place the pan on a wire rack to cool. The cake should cool for at least 1 hour before serving, I actually prefer it after it has set for a day, so it's a great recipe to make in advance.