Preheat the oven to 425 degrees.

In a large bowl, stir together flour, cornmeal, baking powder, salt, and cayenne. In a second small bowl, whisk together milk, 1/4 cup oil, eggs, cheese, and jalapenos. Add liquid mixture to dry mixture and stir just to combine.

In an 8-inch cast-iron skillet, heat 1 tablespoon vegetable oil. Spoon batter into skillet. Bake until a toothpick inserted into center comes out clean and top has lightly browned, about 20 to 25 minutes. Brush honey and butter over top and let cool briefly before serving.