Preheat oven to 350 degrees F (175 degrees C). Grease 30 muffin cups.
Blend turkey in a food processor until pureed. Mix flour, white sugar, turkey, butter, canola oil, baking powder, vanilla extract, and salt together in a large bowl until all batter is moistened. Pour batter into the prepared muffin cups, filling them about 2/3 full.
Bake in the preheated oven until a toothpick inserted into the center of a muffin comes out clean, 20 to 25 minutes. Cool muffins in the tins for 10 minutes before removing to cool completely on a wire rack.
Mix confectioners' sugar and gravy together in a bowl until glaze is smooth. Spoon glaze onto cooled cupcakes.