Position a rack in the center of the oven and preheat the oven to 400 degrees F. Generously coat a 9-inch square baking dish or 9-inch cast-iron skillet with cooking spray.
Whisk together the cornmeal, flour, sugar, baking powder, baking soda and salt in a large bowl. Whisk together the milk, sour cream, butter and egg in a medium bowl. Add the milk mixture to the flour mixture and whisk to combine. Fold in the cherries, Gouda and ham.
Pour the batter into the prepared baking dish and bake until the cornbread springs back when pressed in the center, 25 to 35 minutes. Let cool in the baking dish for about 15 minutes. Loosen the edges, then slice into squares or wedges and serve warm or at room temperature.
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