Preheat oven to 425°F. Place 2 (7-stick [5 1/2-inch-long]) cast-iron corn stick pans on a rimmed baking sheet. Transfer baking sheet to oven. Preheat 15 minutes.

Meanwhile, whisk together flour, cornmeal, baking powder, and salt in a bowl; set aside.

Cook corn, jalapeño, scallions, and 8 tablespoons of the butter in a skillet over medium, stirring often, until mixture is softened, about 3 minutes. Set aside; cool 5 minutes.

Whisk together eggs, half-and-half, and sugar in a bowl. Add to flour mixture, whisking until smooth. Stir in jalapeño mixture and cheese.

Remove hot corn stick pans from oven. Brush molds evenly with remaining 2 tablespoons butter. Divide batter evenly among molds (about 3 tablespoons each). Bake until sticks are puffed and golden brown, 14 to 16 minutes. Serve warm, or turn sticks out onto a wire rack and cool completely, about 30 minutes.