To a glass measuring cup, combine instant yeast with warmed half-n-half (or milk). Make sure the liquid is between 110-115 degrees F. Check the directions on the back of the yeast package to see the exact temperature for that yeast product, to be mixed with liquids.
To a mixer or bowl, combine flour, brown sugar, pumpkin spice, pumpkin puree, butter, salt, and eggs.
Combine the milk and yeast mixture with the rest of the dough ingredients and run mixer (or hand mix) for 5-7 minutes to form a ball of dough.
Cover the mixing bowl with plastic wrap. Leave dough to rise for 1 hour or until it is approximately twice it's size.
When ready, preheat oven to 400 degrees F and spray a 9x13 pan with nonstick spray. Lightly flour your countertop to roll.
Roll the dough out into a 16" x 22" rectangle that is approximately 1/4" thick. Coat with the melted butter from edge to edge, covering completely. Sprinkle with brown sugar, cinnamon, and pumpkin spice all over, from edge to edge.
Carefully roll the longer bottom edge to the top edge, so that the roll is approximately 22" long. Start by slicing down the center, creating two halves. Then slice down the center of those halves, and so forth. I find it's easier to get more consistently even slices this way. You should have 12 rolls total.
Place each roll into the prepared baking dish and bake 15-20 minutes. I found they were perfect at 15 minutes, but I like mine a teensy bit gooey. Check at 15 minutes.
While the cinnamon rolls are cooling, combine the cream cheese, powdered sugar, vanilla extract, and half-n-half into a mixing bowl. Add the half-n-half 1 tablespoon at a time. Some may like their frosting thick, while some may like it more thinned out.
Spread the frosting over the top of the rolls, making sure to cover each one thoroughly.