Step 1: Preheat your oven to 400°F (200°C). Lightly grease a corn stick pan (if using) or line a baking sheet with parchment paper. If using a corn stick pan, place it in the oven for 5-10 minutes to preheat.
Step 2: In a large mixing bowl, combine the all-purpose flour, yellow cornmeal, baking powder, sugar, salt, and black pepper. Whisk these dry ingredients together thoroughly.
Step 3: In a separate medium bowl, whisk together the milk, melted unsalted butter, and egg until well combined.
Step 4: Pour the wet ingredients into the dry ingredients. Mix with a spatula until just combined. Be careful not to overmix; a few lumps are fine.
Step 5: Gently fold in the corn kernels, shredded cheddar cheese, and shredded mozzarella cheese until evenly distributed throughout the batter.
Step 6: Carefully spoon the batter into the preheated and greased corn stick pan, filling each cavity about two-thirds full. If not using a corn stick pan, drop spoonfuls of batter onto the prepared baking sheet and shape them into small log-like sticks (about 3-4 inches long and 1 inch wide).
Step 7: Bake for 18-22 minutes, or until the corn sticks are golden brown on the edges and cooked through. They should feel firm to the touch, and a toothpick inserted into the center should come out clean.
Step 8: Once baked, remove the pan from the oven and let the corn sticks cool in the pan for 5 minutes before carefully transferring them to a wire rack to cool slightly. Serve warm.