Warm 1/2 cup eggnog in a small saucepan over low heat until it bubbles, about 5 minutes. Remove from heat and mix in 1/8 cup butter and 1/8 cup pumpkin; stir until melted. Add water and let mixture cool until lukewarm, about 5 minutes.
Combine cooled eggnog mixture, 1 cup flour, white sugar, egg, yeast, and salt in a large bowl. Stir well to combine. Stir in remaining flour 1 cup at a time, beating well after each addition with an electric mixer until dough has pulled together. Turn dough out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.
Roll dough into a 12×9-inch rectangle.
Combine brown sugar, cinnamon, nutmeg, cloves, and allspice together in a bowl. Spread melted butter on top of dough and top with brown sugar mixture. Roll dough into a log, using a little water to seal the seam.
Cut roll into 12 slices using a very sharp knife or a piece of unflavored dental floss. Place rolls into a 9×13-inch greased baking pan. Cover and let rise until almost doubled in size, about 1 hour.
Preheat the oven to 375 degrees F (190 degrees C).
Bake in the preheated oven until golden brown, 20 to 25 minutes.
Meanwhile, combine confectioners’ sugar, cream cheese, 1/4 cup pumpkin, and vanilla extract in a bowl. Add eggnog gradually until frosting reaches a spreadable consistency. Spread frosting over warm cinnamon rolls.
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