1. Make the Dough: In a glass measuring cup, heat the milk in the microwave until warm, 1 minute. In the bowl of a standing electric mixer fitted with the paddle, combine the warm milk and the yeast. Add the granulated sugar and the 6 tablespoons of softened butter and mix at medium speed until the butter is broken up, 1 minute. Beat in the eggs, one at a time. Add the flour and salt and mix at low speed until incorporated, about 2 minutes. Scrape down the side of the bowl. Increase the speed to medium and mix the dough for 2 minutes longer. Scrape the dough into a lightly oiled bowl, cover with plastic wrap and let stand at room temperature for 30 minutes.
2. Preheat the oven to 325°. Spray a standard 12-cup muffin tin with nonstick cooking spray.
3. On a lightly floured work surface, roll the dough out to a 9-by-24-inch rectangle. In a small bowl, mix the light brown sugar with the cinnamon. Brush the 2 tablespoons of melted butter over the dough and sprinkle with the cinnamon sugar. Beginning at a long edge, roll up the dough as tightly as possible and pinch the seam. Cut the log into twelve 2-inch pieces and set them in the muffin cups cut side up. Cover and let stand in a warm place for 30 minutes.
4. Set the muffin pan on a baking sheet and bake for 25 to 30 minutes, until the buns are golden brown. Spread the pecans in a pie plate and toast for 10 minutes, until fragrant. Let cool, then coarsely chop the nuts.