Preheat the oven to 350° and fill 12 muffin cups with paper liners. In a small saucepan, combine the blueberries with 1 teaspoon of the sugar and cook over moderate heat, crushing and mashing with a spoon, until the blueberry compote is reduced to 1/4 cup, about 5 minutes. Let cool.
In a medium bowl, whisk the cornmeal with the flour, baking powder, salt, baking soda and the remaining 1/4 cup of sugar. Add the eggs, sour cream, melted butter and milk and whisk until combined.
Spoon the batter into the muffin cups and top with the blueberry compote. Using a toothpick, swirl the compote into the batter, then sprinkle with sugar.
Bake the muffins in the center of the oven for 20 minutes, until a toothpick inserted into the center comes out clean. Let cool slightly before serving.