Preheat your oven to 375°F. Grease 12 muffin cups generously; a vegetable oil pan spray works well.
In a large mixing bowl, cream together the butter and sugar until they're light and fluffy. Add the eggs, one at a time, beating well after each addition. In a separate bowl, whisk together the flour, baking powder and salt. Add the dry ingredients to the creamed mixture, and beat well. Stir in the milk and vanilla. mixing only until smooth. Quickly stir in the berries.
Fill the muffin cups 3/4 to almost full, using all of the batter. Sprinkle with the cinnamon sugar. Bake the muffins for 30 minutes, until they're light golden brown, remove them from the oven, and place the pan on a rack to cool for 10 minutes. After 10 minutes, run a knife around the edge of one muffin, and try to lift it out of the pan. (These muffins are very tender, and if they don't cool long enough, they'll crumble when you try to remove them from the pan.) If the muffin lifts out of the pan without crumbling, remove all of the muffins and cool them completely on a wire rack. If the muffin sticks or the top peels off, allow them to cool an additional 10 minutes, then try again.