Preheat your oven to 375°F (190°C) and line a 12-cup standard muffin tin with paper liners or grease the cups generously with butter.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt until they are fully combined and free of lumps.
In a separate medium bowl, beat the egg with a fork, then whisk in the milk, melted butter, and vanilla extract until the mixture is smooth and uniform.
Pour the wet ingredients into the dry ingredients and stir with a spatula until the batter is just combined; a few streaks of flour are okay and the batter will be slightly lumpy to prevent overmixing.
Gently fold the chopped cranberries into the batter until they are evenly distributed throughout.
Divide the batter evenly among the 12 prepared muffin cups, filling each about 3/4 full, and sprinkle the top of each one with the coarse sugar.
Bake for 20 to 25 minutes, or until the muffins are golden brown on top and a toothpick inserted into the center of one comes out clean with no wet batter.
Let the muffins cool in the pan on a wire rack for 5 minutes before transferring them directly to the rack to cool completely.