Preheat the oven to 350 degrees.  Grease a 9 x 9-inch square baking pan.

In a large bowl, combine the flour, cornmeal, sugar, baking powder, and salt. In separate bowl, whisk together the milk, egg and egg yolk, and melted butter.

With a wooden spoon, stir the wet ingredients into the dry until most of the lumps are dissolved. Don't overmix. Stir in 1 cup of the cheese along with the green onions and jalapenos. Allow the mixture to sit at room temperature for 10-15 minutes.

Pour the batter into the prepared pan and smooth the top. Sprinkle with the remaining cheese.  Bake for about 23 minutes, or until a toothpick inserted into the center comes out clean. Place on a wire rack to cool slightly before slicing and serving.