Pour buttermilk into a small saucepan. Heat to approximately 110 degrees F. Pour into a large liquid measuring cup. Stir yeast and 1 tablespoon sugar into the buttermilk. Let the mixture sit until foamy bubbles appear on the surface of the buttermilk, about 10 minutes.
Whisk in eggs and the cooled melted butter.
The next part can be done with a stand-mixer orby hand. In the bowl of a mixer with a dough hook, combine 4 cups all-purpose flour, 3 tablespoons sugar, salt, and cinnamon. Turn the mixer on low for about 10 seconds to mix the ingredients.
With the mixer set on low, slowly add the buttermilk mixture. Mix until the ingredients form into a dough.
Turn the mixer to medium and knead until the dough is smooth and elastic, 5 to 7 minutes. The dough should be pulling away from the sides of the bowl. If the dough is still sticking to the sides of the bowl, mix in more flour, 1 tablespoon at a time, until the dough reaches the desired consistency.
Turn the dough onto a clean surface and add currants (or raisins). Knead the currants into the dough until they are evenly dispersed.
Place the dough into a bowl coated with cooking spray. Cover with plastic wrap and place in a warm, draft-free place until the dough doubles in size, 2 to 2 ½ hours.
Turn the dough onto a lightly floured surface and divide the dough into 12 pieces. With the palm of your hand, roll each ball to form a ball. Coat a 9- by 13-inch baking pan with cooking spray.
Place the 12 balls of dough into the pan. Wrap tightly with greased plastic wrap. Let the dough rise in a warm, draft-free place for 1 to 1 ½ hours, or until the rolls double in size and are pressed against each other.
Preheat the oven to 350 degrees F with the rack in the middle position.
Using a small, sharp knife, cut a ¼-inch deep X through the top of each bun. In a small bowl, whisk together egg and water. Brush the tops of the buns with the egg mixture.
Bake for 25 to 30 minutes, or until the buns are puffed and golden brown. Sit the pan on a cooling rack and let the buns cool in the pan for 5 minutes.
Whisk together powdered sugar, milk, and vanilla. Using a small spoon, drizzle the glaze over top of the buns in an X, in the grooves on the buns. Serve warm or cool to room temperature.
Once you place the balls of dough in the baking pan, do not let the dough rise. Instead, store in the refrigerator overnight, up to 16 hours. Before baking, let the buns sit at room temperature until they double in size, 1 to 1 ½ hours.