Preheat the oven to 350°F (175°C). Grease your cake pan with a little butter or corn oil.
Cream the sugars and butter. In a large bowl, beat the brown sugar, white sugar, and butter together until light and fluffy.
Add the eggs and vanilla. Beat in the eggs one at a time, mixing well after each. Stir in the vanilla extract and corn oil.
Mix the dry ingredients. In another bowl, whisk together the flour, baking powder, and kosher salt.
Combine the wet and dry ingredients. Gradually add the dry mixture into the wet mixture, alternating with the half and half. Mix just until combined—don’t overmix!
Fold in the corn kernels. Gently stir them in with a spatula to distribute evenly.
Pour into the pan. Spread the batter evenly in your prepared pan.
Bake. Bake for 40–45 minutes, or until a toothpick inserted into the center comes out clean.
Cool and serve. Let the cake cool in the pan for about 15 minutes before transferring it to a wire rack. Dust with powdered sugar or serve with vanilla ice cream if you like!