Pecan Currant Sticky Buns

I bought a whole cookbook just for this recipe - they are to die for!!!
DOUGH
1 1/2 Cups warm milk
2 packages yeast (almost 2 TBS)
1/3 cup sugar
5 1/4 Cups flour
2 tsp salt
2 large eggs
1/2 stick (4 TBS )unsalted butter softened

FILLING
2/3 Cup packed dark brown sugar (I use light)
2/3 Cup dried currants (I leave these out)
2/3 Cup chopped pecans
1 tsp ground cinnamon
1/2 stick (4 TBS) unsalted butter softened

SYRUP
1 stick (8 TBS) unsalted butter cut into pieces
1/2 Cup packed dark brown sugar (I use light)
1/2 Cup sugar
2 TBS light corn syrup
1/4 Cup heavy cream

Make the dough: Stir together 1/2 cup warm milk, yeast, and pinch of sugar in a small bowl until yeast is dissolved. Let stand until foamy, about 5 minutes.
Put flour, remaining sugar, and salt in mixer bowl and mix with dough hook at low speed until combined. Whisk together remaining 1 Cup milk and eggs in a small bowl, then add to dry ingredients, along with yeast mixture and mix at medium speed until a very soft dough forms about 2 minutes. Add butter and continue beating until dough is smooth and elastic about 4 minutes (dough will be very sticky).
Rinse a large bowl with hot water, then put dough in wet bowl and cover tightly with plastic wrap. Let dough rise in a warm draft-free place until doubled in bulk about 1 1/4 hours.
Prepare the filling: Stir together all ingredients except butter in a small bowl.
Make the syrup: Butter muffin cups. Combine butter, sugars, corn syrup and heavy cream in a 1 quart saucepan and heat over low heat , stirring, until butter is melted. Bring to a simmer and simmer, stirring, for 2 minutes. Spoon 2 TBS warm syrup into each muffin cup.

Fill and form the buns. Turn dough out on a well-floured surface and dust with flour . Roll into a 16 by 12 inch rectangle with a floured rolling pin. Turn dough if necessary so long side is nearest you. Brush off excess flour, then spread evenly with softened butter. Sprinkle filling evenly over dough. Beginning with long side near you, roll up dough to form a 16 inch long log and press seam to seal.
Cut log crosswise into 12 rounds. Arrange buns cut side up in muffin cups. Cover with oiled plastic wrap and let rise in a warm draft-free place until double in bulk about 1 hour.
Put rack in middle of oven and preheat oven to 350.
Bake buns until puffed and golden, 30-35 minutes. Cool in pan on a rack for 10 minutes, then invert buns onto rack and cool slightly. Serve warm.