Preheat the oven to 350 degrees F. Butter an 8-inch square baking dish that is at least 2 inches deep. Place the buttered dish in the oven while you mix the batter.
Whisk together the heavy cream, 1 teaspoon of the sugar and 1/2 teaspoon salt in a small bowl and set aside.
Whisk together the eggs and melted butter in a large bowl until well blended. Add the milk, vinegar, the remaining sugar and 1 teaspoon salt and beat until mixed well. Whisk together the cornmeal, flour, baking powder and baking soda in a medium bowl.
Add the flour mixture to the egg mixture and stir until just combined. Pour the batter into the preheated dish, then slowly, pour the seasoned cream into the center of the batter about 1-inch away from the edge. Don't stir the cream into the batter.
Bake until the top of the cornbread is lightly browned, and a toothpick inserted near the edge of the bread (not the center) comes out clean, about 50 minutes. Serve warm.
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