Whisk brown sugar and 1 1/2 teaspoons cinnamon together in a shallow bowl. Dip each piece of butter into cinnamon-sugar mixture to coat completely. Place butter pieces in a single layer on a parchment paper-lined baking sheet. Freeze until hard, 8 hours to overnight.
Stir 1 cup flour, 2 teaspoons cinnamon, baking powder, and salt together in a bowl. Beat buttermilk, eggs, and white sugar together in another bowl; add flour mixture to buttermilk mixture and beat until smooth. Gradually stir remaining flour into buttermilk mixture until desired batter consistency is reached.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Poke a toothpick into the center of each frozen piece of butter. Dip butter into batter to coat completely.
Working in batches, carefully drop coated butter pieces into hot oil and cook, turning occasionally, until golden brown and puffed, about 2 minutes. Transfer fried butter to a paper-towel lined plate and dust with confectioners’ sugar.