Heat the milk in a small saucepan over medium heat until it just begins to boil. Remove from heat and let stand until cooled to room temperature. Meanwhile, sprinkle the yeast over the warm water in a large bowl. Add 1 tablespoon of the sugar and let stand until foamy, about 5 minutes.
Beat in the remaining 2 tablespoons sugar, eggs and butter. Beat in cooled milk. Gradually add the flour and salt, scraping down side of bowl, until a soft dough forms. Turn dough onto a floured work surface and knead the remaining flour into the dough, adding more flour if too sticky. Knead for about 10 minutes until smooth. The dough will be soft.
Grease a large bowl. Place the dough in the bowl. Cover with plastic wrap and place in a warm spot until doubled in size, about 1 1/2 hours-2 hours.
In a small bowl, stir together all of the ingredients for the filling. Coat two 9-inch round baking pans with nonstick cooking spray. Line bottoms with parchment paper; coat paper with spray.
Punch down the dough. Dump the dough out onto a floured surface, roll out the dough into a 10-by-18-inch rectangle. Spread the cheddar mixture over the dough, leaving a 1-inch border on the sides. Brush the borders with water. Tightly roll the dough into an 18-inch log, rolling toward the clean border; pinch the seam to seal.
Cut crosswise into 12 generous 1 1/2 inch pieces.
Arrange 6 pieces in each prepared pan.
Brush the rolls with the remaining melted butter. Cover with plastic wrap and let sit in a warm spot until buns double in size, about 30 to 45 minutes.
Heat oven to 350°F.
Uncover pans and bake buns until they are golden-brown and bubbly, 30 to 40 minutes.
Transfer to a wire rack and let cool 10 minutes