Wash pots with soap and water, and dry well. Line pots with cooking parchment: Gently push center of a square into each pot; bend parchment edges outward slightly over edges of pots.
In a small bowl, mix flour, cornmeal, baking powder, baking soda, and salt.
In another bowl, beat eggs and sugar until well blended. Add flour mixture, yogurt, onions, and melted butter; stir just until batter is evenly moistened.
Spoon batter equally into lined pots, filling pots almost to the top. Sprinkle with caraway seed. Set pots slightly apart in a 9- by 13-inch baking pan.
Bake muffins in a 400° regular or 375° convection oven until tops are lightly browned and centers are firm to touch, 18 to 20 minutes. Let muffins cool in pots 5 to 10 minutes.
Serve warm, or invert pots to remove muffins and lay on their sides on racks to cool. Serve muffins in parchment liners.
Nutritional analysis per muffin.