Preheat oven to 400-degrees F. Line a standard muffin pan with paper cups.
Whisk flour, baking powder, baking soda salt, and cinnamon in a large bowl. In a separate bowl, whisk together eggs, yogurt, sugar, oil, and vanilla. Add flour mixture and mix with light strokes until the dry ingredients are just moistened. Do not overmix; batter will not be smooth.
Divide batter among the muffin cups and bake until a toothpick inserted in one or two of the muffins come out clean, 12-15 minutes.
While the muffins are baking, melt butter and place in a bowl just large enough to hold a muffin. Combine sugar and cinnamon in a small, shallow bowl. As soon as the muffins are done, dip them one at a time in the melted butter and then roll in the sugar mixture. Set on a rack to cool.
To make buttercream:
Beat butter, powdered sugar and cocoa at medium speed until fluffy.
Microwave whipping cream until warm (do not boil), about 15-20 secs. Stir together warm cream and coffee granules until dissolved; cool. Slowly add coffee-cream mixture in 1 tsp increments and liqueur to butter mixture, beating until smooth. You may not use all of the coffee/cream mixture, just use what you need until you get the consistency you like.