Step 1Stir together one-half cup warm milk, yeast and a pinch of sugar in a small bowl until the yeast is dissolved. Let stand until foamy, about 5 minutes. (If mixture doesn't foam, discard and start with new yeast.)
Step 2Put the flour, remaining sugar and salt in a mixer bowl and mix with a dough hook at low speed until combined.
Step 3Whisk together the remaining 1 cup milk and the eggs in a small bowl, then add to dry ingredients along with the yeast mixture and mix at medium speed until a very soft dough forms, about 2 minutes. Add the butter and continue beating until the dough is smooth and elastic, about 4 minutes (dough will be very sticky).
Step 4Rinse a large bowl with hot water, then put the dough in the wet bowl and cover tightly with plastic wrap. Let the dough rise in a warm draft-free place until doubled in bulk, about 1 1/4 hours.
Step 1Stir together all of the ingredients in a small bowl.
Step 1Combine the one-half cup butter, sugars, corn syrup and heavy cream in a 1-quart saucepan and heat over low heat, stirring, until the butter is melted. Bring to a simmer and simmer, stirring, for 2 minutes.
Step 1Butter the muffin cups. Spoon 2 tablespoons warm syrup into each muffin cup.
Step 2Turn the dough onto a well-floured surface and dust with flour. Roll out into a 16- by-12-inch rectangle with a floured rolling pin. Turn the dough if necessary so the long side is nearest you. Brush off the excess flour, then spread evenly with the softened butter.
Step 3Sprinkle the filling evenly over the dough. Beginning with the long side near you, roll up the dough to form a 16-inch-long log and press the seam to seal.
Step 4Cut the log crosswise into 12 rounds. Arrange the buns cut sides up in the muffin cups. Cover loosely with oiled plastic wrap and let rise in a warm draft-free place until doubled in bulk, about 1 hour.
Step 5Put a rack in the middle of the oven and heat the oven to 350 degrees. Bake the buns until puffed and golden, 30 to 35 minutes. Cool in the pan on a rack for 10 minutes, then invert the buns onto a rack and cool slightly. Serve warm.