Sift together flour, cream of wheat, sugar, baking soda, baking powder, and salt in a large bowl; set aside. Whisk together milk, sour cream, vegetable oil, egg, and vanilla in a separate bowl until well combined. Make a well in the center of flour mixture and stir in milk mixture; do not overmix batter.

Heat a large skillet over medium heat. Pour 1/3 cupfuls of batter onto the hot skillet and cook until bubbles appear on the surface. Flip with a spatula and cook until browned on the other side. Repeat with remaining batter.