In a large bowl, stir yeast into water to soften. Let rest for 5 minutes before stirring. Mix Egg & add milk, pumpkin, butter, 1 1/4 cups whole wheat white flour, brown sugar, salt, cinnamon, ginger, nutmeg and cardamom to yeast mixture. Beat vigorously for 2 minutes. Gradually add remaining flour (all purpose), a little at a time, until you have a dough stiff enough to knead. Start with about 1 1/2 cups and increase if necessary. Turn dough out onto a floured surface. Knead, adding flour as necessary, until you have a smooth, elastic dough. Put dough into an oiled bowl. Turn once to coat entire ball of dough with oil. Cover with a towel and let rise until doubled, about 1 hour.
Combine the white sugar, brown sugar, cinnamon, allspice, ginger, nutmeg and cloves in a small bowl, set aside. Transfer the risen dough to a lightly greased work surface, and pat or roll it into a 16" x 12" rectangle. Spread softened butter over dough and then sprinkle with the sugar mixture. Roll the dough into a log the long way; it'll stretch to about 20" long as you roll. Using a very sharp knife, slice the log into 15 slices. It helps to rinse the blade in hot water, and wipe it off, between slices. Place slices in a greased 9x13 inch baking pan (or in two 8 or 9 inch round cake or pie pans). Cover with a towel and let rise until almost doubled, about 45 minutes. Bake in a preheated 375°F oven. Bake the rolls till they're brown around the edges and beginning to turn golden brown across the center, about 20-30 minutes.
While rolls bake, prepare the cream cheese frosting. Add the cream cheese, vanilla, milk and pumpkin to a small food processor or use an immersion blender. Blend until
smooth and combined. Add the powdered sugar 1/2 cup at a time, blending in between, until well mixed and desired consistency is reached. Frost warm rolls with the cream cheese frosting and serve immediately! Great with a cup of your favorite coffee.