1/4 cup butter, plus 2 tablespoons for coating the pan
Preheat the oven to 350ºF. Melt two tablespoons of butter in a small saucepan over medium heat or in a small bowl in the microwave for about 30 seconds. Use a pastry brush to generously coat the cups of a 12-cup muffin pan.
Place the flour, 2/3 cup of the sugar, the baking powder, and salt in the bowl of a stand mixer fitted with the paddle attachment. Give a couple of turns on low to combine.
Add the eggs, buttermilk, oil, and vanilla and beat on medium until just combined. Use a large ice-cream scoop to divide the batter evenly between the prepared muffin cups.
Bake for 15 to 20 minutes or until a wooden skewer inserted in the center of a muffin comes out clean. Meanwhile, place the remaining sugar and the cinnamon in a medium bowl and stir to combine. Set aside.
Melt the remaining butter in a small saucepan over medium heat or in a small bowl in the microwave for about 30 seconds. Set aside to cool.
Remove the muffins from the oven and allow to cool for only a minute or so. Use a pastry brush to coat each muffin with melted butter and then roll each one in a little cinnamon sugar.
Store tightly wrapped in an airtight container for up to three days, or in the freezer for up to three months