Preheat the oven to 400 F. Grease muffin pans or line them with paper baking cups. Stir and toss together the flour, baking powder, and salt until completely mixed. Place the sugar, eggs, milk, butter, and vanilla in a large bowl and mix well.
Add the combined dry ingredients and beat just until the batter is blended; it should not be completely smooth. Spoon the batter into the prepared muffin pans, filling each cup about two-thirds full. Bake for about 20 minutes, or until a toothpick inserted in the center of a muffin comes out clean. Remove from the pans and serve warm.