Heat milk until it is just slightly warm to the touch. Whisk with sugar and yeast in a large mixing bowl and let stand for 5 minutes. Add eggs and 8 Tbsp. softened butter and mix well. Add 4 and ¼ cups flour and salt and mix until ingredients come together into a soft, pliable dough.
Turn dough out onto a lightly floured surface and knead until it becomes smooth and slightly shiny, about 10 minutes. (While kneading, add additional flour a bit at a time to prevent dough from sticking to your hands, if needed.) Place dough in a medium mixing bowl that has been lightly greased with ½ Tbsp. softened butter and cover with plastic wrap. Allow dough to rise at room temperature until doubled in size, about 2 hours.
Roll the dough out on a lightly floured surface into a 12-by-24-inch rectangle, with long sides at the top and bottom. Spread 2 Tbsp. softened butter over the surface of the dough. Evenly pour apple butter over the dough, followed by ¼ cup dark brown sugar, and finally pecans. (Don't worry if the toppings are not spread evenly.) Starting at the bottom of the roll (the side closest to you), roll the dough tightly into a log.
Using remaining 1 and ½ Tbsp. butter, grease the sides and bottom of a 9-by-13-inch baking pan. Sprinkle the remaining ¼ cup dark brown sugar over the butter in the bottom of the baking dish. Cut dough into 12 even slices. Arrange the slices evenly in the prepared baking dish. (At this point you can cover the pan and refrigerate overnight if you prefer to serve it the next morning.) Allow rolls to to rise in the pan at room temperature for 2 hours.
Preheat oven to 350°. Bake rolls until tops are light brown and filling is bubbling, about 30 minutes.
Allow to cool at room temperature for 10 minutes and invert pan over a cutting board or serving dish. Serve warm.
The recipe for the dough used above is adapted from Raspberry Swirl Sweet Rolls by Grace Parisi, published in the January 2011 edition of Food and Wine.
Note: You will notice in my pictures above that I opted to line the bottom of my baking dish with parchment paper - this is optional, but makes clean-up a bit easier. Although this recipe makes 12 sticky buns, these are a great thing to split up into smaller batches. I baked 9 rolls in a 9x9 baking dish and popped the remaining slices into a small well-sealed tin in the freezer. You can freeze the whole thing for up to a month after step 3. Just wrap the rolled log of dough tightly and freeze. When you are ready to make them, let them warm at room temperature until you can easily slice them and continue with step 4, above. Before cutting the log into 12 slices for baking, I like to cut off about 1 inch of the uneven ends. After I've arranged the 12 slices in the baking pan, I roll the end bits into balls and place them in the baking pan, between the rolls. These become tasty little nubs that are the perfect size when you don't have room for another sticky bun, but still want one more bite...