Heat the oven to 350 degrees and grease 2 (12-cup) muffin pans or tins.
In a large bowl, whisk together the flour, baking powder, salt, and 1 tablespoon espresso powder. In a separate bowl or large measuring cup, combine the coffee, buttermilk, and vanilla. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a hand mixer, beat together 1 1/2 cups softened butter with 2 cups (14 ounces) sugar until light and fluffy, 3 to 5 minutes. Beat in the eggs, one at a time, waiting until each egg is fully incorporated before adding another.
Gently beat the flour and coffee mixtures into the butter mixture, alternating between wet and dry, one-third of each at a time. Scrape down the sides of the bowl as needed to make sure all of the ingredients are properly mixed.
Divide the batter among each of the greased muffin cups, filling each approximately two-thirds to three-fourths of the way full. Place the pan in the oven and bake until the muffins have risen and a toothpick inserted comes out clean, 20 to 30 minutes. Rotate the pan halfway through for even baking. Remove the muffins and cool completely.
Meanwhile, in a medium bowl, combine the remaining 1 1/2 cups (10 1/2 ounces) sugar and 1 to 2 tablespoons espresso powder. Brush the cooled muffins on all sides with the melted butter, then roll in the sugar/espresso powder mixture. Serve immediately.