Chop onions and drain over a bowl in a fine mess strainer.
Grate cheese and mix 1 cup into the dry ingredients.
Add ¾ cup of drained onions to the bowl and mix well being sure the cheese and onions do not clump up but are evenly distributed.
Mix milk, egg, butter together in a small bowl. Pour into dry ingredients and mix gently until all the flour is moistened.
Fill each well of a muffin pan evenly. Sprinkle about a ¼ teaspoon of reserved chopped onions over the top of each muffin. Sprinkle remaing cheddar cheese over each muffin top.