In a large mixing bowl sift together all dry ingredients: flour, sugar, salt, and baking powder. Give the mixture a quick whisk to make sure they are all evenly distributed.
In a separate bowl whisk together wet ingredients: milk, eggs, and butter. Pour the wet ingredients into the dry ingredients.
Using a rubber spatula quickly mix just until the dry ingredients are moistened. The batter will come out lumpy! Fill muffin tins about 3/4 full. Bake for about 15-20 minutes, until a toothpick comes out clean from the center.
In a food processor puree the blueberries, add the powdered sugar, and process until creamy and smooth. Add additional icing sugar if needed. Spread a generous amount of icing on each muffin and place on a rack or parchment paper to drip.