Position a rack in the center of the oven and preheat the oven to 350°F. Lightly oil a 9 × 13-inch baking dish.

In a medium saucepan, heat the oil over medium heat. Add the onion and jalapeno, and cook, stirring often, until the onion is golden, about 4 minutes. Add the garlic and stir until fragrant, about 1 minute. Sprinkle with the flour and chili powder, and stir until vegetables are coated.

Gradually stir in the broth, then the tomato sauce and ¼ teaspoon salt. Bring to a simmer, then reduce the heat to medium-low. Simmer, stirring often to avoid scorching, until the sauce thickens, about 5 minutes. Stir in the turkey, black beans, and corn. Pour into the prepared dish.

In another medium saucepan, bring 1½ cups water and the remaining ¾ teaspoon salt to a boil over high heat. In a small bowl, whisk the cornmeal with 1½ cups cold water. Whisk into the boiling water and cook, whisking constantly, until the mixture is thick and boiling, about 1 minute. Spread over the turkey mixture as smoothly as possible. Sprinkle with the cheese.

Bake until the turkey mixture is bubbling, about 30 minutes. Let stand for 5 minutes before serving.