Preheat the oven to 350 degrees F. Place 16 paper liners in muffin pans.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugar until light and fluffy, about 5 minutes. With the mixer on low speed, add the eggs 1 at a time, then add the vanilla, sour cream, and milk. In a separate bowl, sift together the flour, baking powder, baking soda, and salt. With the mixer on low speed add the flour mixture to the batter and beat until just mixed. Fold in the blueberries with a spatula and be sure the batter is completely mixed.
Scoop the batter into the prepared muffin pans, filling each cup just over the top, and bake for 25 to 30 minutes, until the muffins are lightly browned on top and a cake tester comes out clean.
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