Preheat the oven to 425ºF (220ºC). Generously grease an 8-inch (20-cm) square baking dish with 2 tablespoons butter, then dust lightly with cornmeal. Set aside.
In a small pot or microwave-safe dish, gently melt ¼ cup butter, then set aside to cool slightly.
Whisk the flour, cornmeal, sugar, baking powder, salt, and baking soda in a mixing bowl.
Whisk the buttermilk and eggs in a measuring cup or bowl.
Pour the buttermilk mixture into the flour mixture. Pour the melted butter on top. Stir until the flour is just mixed in and the cornmeal is evenly distributed.
Pour the batter into the prepared dish, smoothing the top. Bake for 25 minutes, or until the top is golden and set. Transfer the cake to a wire rack to cool slightly before slicing into squares. Serve warm with butter, maple syrup, or molasses.
Notes
When greasing the pan, leave a little extra butter in the corners to prevent sticking.
Stir the batter gently, stopping as soon as the flour is incorporated to avoid overmixing. A few streaks of flour are fine.
Let the cake cool for at least 20 minutes before slicing so the crumb can set.
Use a thin, sharp knife to cut neat squares without dragging crumbs across the top.
Storage
Keep the cake in an airtight container at room temperature for up to 2 days, or in the refrigerator for up to 5 days. Warm slices gently in the oven or microwave before serving.
Store individual slices in the freezer inside a zipper-top bag or container with a tight-fitting lid for up to 2 months. Thaw at room temperature or reheat gently in the oven or microwave.