For the rolls
In a small saucepan, warm the milk over low-medium heat until it reaches 180ºF. Set aside and let cool to 100ºF-115ºF or until warm to the touch. Alternatively, microwave in a heat-proof glass measuring cup for 15-second intervals until the milk reaches 180ºF.
In a medium bowl, whisk together the flour, instant yeast, light brown sugar, cinnamon, and salt. Set aside.
In a separate bowl, whisk the warm milk, pumpkin puree, melted butter, and beaten egg together.
Add the dry mixture to the wet ingredients and mix with a spatula until the dough starts to form.
Transfer the dough to a mixing bowl fitted with a dough hook and knead at low speed for 7-8 minutes until the dough comes together. It should be soft, slightly sticky, and pulling away from the bowl sides.
If still too sticky, add up to 1/4 cup additional flour, one tablespoon at a time.
Alternatively, stir the dough by hand using a Danish dough whisk.
Turn the dough out onto a lightly floured surface and knead into a soft, smooth ball. Transfer it to a lightly greased medium bowl, cover with plastic wrap or a clean tea towel, and place in a warm spot to rise until doubled in size (about 1 hour).
If resting the dough in the oven, do not use plastic wrap (see notes).
For the cinnamon spice filling
In a small bowl, combine light brown sugar, granulated sugar, cinnamon, ginger, nutmeg, allspice, and cloves. Set aside. The room temperature butter will be spread on the dough during assembly.
Assembling the rolls
Lightly spray an 1/8 sheet pan or a 6-inch round or square baking pan with a flour-based baking spray. Set aside.
After the dough has doubled, punch it down with your fist and turn it out onto a lightly floured surface. Lightly flour your rolling pin. Roll the dough into a 10” x 12” rectangle.
Spread the softened butter evenly over the dough, leaving a 1/4-inch border along the edges. Sprinkle the cinnamon spice filling over the buttered surface.
Starting from the longest side, roll the dough tightly into a log.
Using a sharp knife, cut the log into 6 equal rolls. Place them cut side down onto the prepared baking pan. For even rolls, use a ruler to mark slices and trim ends for a clean edge; the ends can be baked separately.
Cover with plastic wrap or a clean kitchen towel and let rise in a warm spot for 25 minutes or until doubled in size. Meanwhile, adjust your oven rack to the second level from the top and preheat the oven to 350ºF.
For overnight preparation, cover the rolls tightly with plastic wrap and refrigerate. Let them come to room temperature and rise for 1 hour before baking.
In a small bowl, beat the egg yolk with water and brush over the rolls. Bake for 20-25 minutes at 350ºF. Cool for 10-15 minutes before frosting.
For the maple frosting
In a small bowl, combine unsalted butter, maple syrup, vanilla extract, milk, and powdered sugar. Mix thoroughly using a hand mixer or stand mixer fitted with a paddle attachment. A hand mixer works best since the frosting quantity is small.
This frosting can be made 1-2 days in advance. Store in an airtight container in the refrigerator and bring to room temperature 20-25 minutes before spreading on the rolls.