Preheat the oven to 375°F. Grease a 12 cup muffin tin or line with cups.
In a medium-sized bowl, beat together the butter and sugar until well combined.
Add eggs one at a time, scraping the sides and bottom of the bowl and beating well after each addition.
Beat in the baking powder, salt, and vanilla.
Add the flour alternately with the milk, beating gently just to combine. Scrape the bottom and sides of the bowl.
Mash 1/2 cup of the blueberries.* Add the mashed and whole berries to the batter, stirring just to combine and distribute.
Use an ice cream or muffin scoop to portion
Sprinkle about a teaspoon of granulated sugar atop each muffin.
Bake the muffins for about 30 minutes, until they're light golden brown on top, and a toothpick inserted into the middle of one of the center muffins comes out clean.
Remove the muffins from the oven, loosen their edges from the pan, and after about 5 minutes transfer them to a rack to cool.
*If you are using frozen berries you don't have to mash some of the berries. To prevent the muffins from turning blue, place your frozen berries in a sieve and run cold water on them until the water runs clear.