In a medium bowl, combine milk and 1 tablespoon sugar. Sprinkle yeast over milk and whisk to blend. Let sit until yeast is foamy, about 5 minutes. Add eggs; whisk until smooth.
In the bowl of a stand mixer fitted with a dough hook, combine remaining 4 tablespoons sugar, flour, and salt. Add the milk mixture. With the mixer running, add butter, 1 piece at a time, blending well between additions.
Mix on medium speed for 1 minute. Knead on medium-high speed until the dough is soft, about 5 minutes.
Brush a medium bowl with some melted butter; place the dough in the bowl. Brush the top of the dough with the remaining melted butter; cover with plastic wrap.
Let dough rise in a warm, draft-free area until doubled in size, about 1 hour.
When you are ready, punch the dough, turn out onto a floured surface, and roll into a 10x15 rectangle (it should be about 1/4 inch thick).
In a medium bowl combine butter, pumpkin puree, brown sugar, pumpkin pie spice, and finely chopped pecans with a fork or spatula. Mix well.
Spread the pumpkin mixture over the dough, leaving a 1/2-inch border at the far edge. Roll the dough up, pinching with your fingers to keep it tightly rolled. Press the seam to seal before positioning the log seam side down.
Use a very sharp knife cut the dough into 12 equal pieces. Place in a greased 9 x 13-inch baking pan.
Place the rolls in a warm dry space and allow them to rise for 1 hour. (They will rise more when baking.)
Bake at 350°F for about 25-30 minutes, or until lightly golden brown. Let cool on a wire rack for at least 5 minutes.
While the rolls cool, mix together the cream cheese, butter, confectioners sugar, and 2 tablespoons of milk on high for about 5 minutes. It should be very smooth and fluffy. If it is not runny enough for your tastes, add another tablespoon of milk. Spread all over the warm rolls and serve.
*If you are using store-bought pumpkin pie spice, use up to 4 teaspoons instead of 2.