For the dough: Combine the milk and 1/2 cup water in a medium saucepan and warm over low heat until it is about 100 degrees F (but no more than 110 degrees). Remove from the heat and sprinkle the yeast over the surface. Sprinkle a pinch of the granulated sugar over the top and let sit without stirring, until foamy, about 5 minutes.
Whisk the butter, vanilla and egg yolk into the yeast mixture.
Whisk together the flour, salt, nutmeg and the remaining granulated sugar in a large bowl. Make a well in the center of the flour and stir in the yeast mixture with a wooden spoon to make a thick and slightly sticky dough. Turn the dough onto a floured work surface and knead until soft and elastic, about 6 minutes. Shape into a ball.
Brush the inside of a large bowl with butter. Put the dough in the buttered bowl, turning to coat lightly. Cover the bowl with plastic wrap and trace a circle the size of the dough on the plastic. Let rise at room temperature until doubled in size, about 1 hour 30 minutes.
Turn the dough out of the bowl and knead briefly to release the excess air; reform into a ball and return to the bowl. Lightly butter a large piece of plastic wrap and lay it on the dough. Cover the entire bowl tightly with the plastic and proof in the refrigerator for 4 hours or up to overnight.
For the filling: Butter a 13-by-9-inch baking pan. Whisk the granulated sugar and cinnamon together in a small bowl. Cut off a 3-inch, or 5-ounce, ball of dough and set aside to make turkey heads. Turn the remaining dough onto a floured work surface and press flat. Then roll into an 18-by-10-inch rectangle, with a long edge facing you. Spread the softened butter evenly over the surface of the dough, leaving about a 1-inch border on the side opposite you. Evenly scatter the cinnamon-sugar over the butter. Starting from the long side facing you, roll the dough up into a tight cylinder. Lightly brush the clean edge of the dough with water. Press this edge against the cylinder to seal.
Slip a long, taut piece of string or unflavored dental floss under the cylinder, about 1 1/2 inches from the end. Lift and cross the string ends over the cylinder, and then pull the ends tightly in opposite directions to cut a single roll. Repeat, cutting every 1 1/2 inches, to make 12 rolls. Place the rolls cut-side-down in the prepared pan, leaving 1 inch of space between them.
Cut the reserved piece of dough into 12 equal pieces. Roll each piece of dough into a 3/4-inch ball. Set each ball of dough aside in a separate baking dish. These will become the turkeys' heads.
Cover the rolls and dough heads loosely with plastic wrap. Set aside in a warm place to rise until both double in size, about 1 hour 30 minutes.
Position a rack in the center of the oven and preheat to 350 degrees F. Using kitchen shears pointing diagonally upward, make a horizontal snip halfway through the front of each ball of dough to form a pointy beak. Pull the beak down a bit to exaggerate the shape. Place a pecan half halfway inside each snip under the beak to form a "waddle." Place two currants above the beak for eyes; press lightly to secure. Place each dough head on top of the lower left hand corner of each cut roll to make turkeys.
Bake the buns until golden brown and the tops of the buns spring back when pressed lightly, about 30 minutes. (Leave the oven on.)
For the glaze: Meanwhile, sift the confectioners' sugar into a medium bowl. Whisk in the condensed milk, butter and vanilla to make a thick, smooth icing. When the buns come out, cool them in the pan for 10 minutes. Drizzle the glaze evenly over all of the bun bodies, but not the heads.
While the buns are cooling, warm the cooked bacon strips in the oven.
To serve, remove each bun turkey from the pan. Slice bacon strips in half. Insert four half-strips of bacon into the back-most cinnamon swirl, so that they form an upright fanned turkey tail.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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