Preheat the oven to 375 degrees F. Grease a muffin tin or line the cups with paper liners. In a mixer fitted with a paddle attachment (or using a hand mixer), cream the butter until smooth. Add 1 cup of the sugar and mix. Add the eggs, vanilla, baking powder, and salt and mix. In a shallow bowl, mash 3/4 cup of the blueberries with the back of a fork. Add to the batter and mix.

With the mixer running at low speed, add 1/2 of the flour, then 1/2 of the milk, and mix. Repeat with remaining flour and milk. Fold in the remaining 1 3/4 cups whole blueberries by hand until well mixed. In a separate small bowl, mix the remaining 2 tablespoons sugar with the cinnamon. Use an ice-cream scoop or large spoon to fill the muffin cups 3/4 full. Sprinkle the cinnamon-sugar over the muffins and bake until golden brown and risen, 25 to 30 minutes. Let cool in the pan at least 30 minutes before turning out.