In a large bowl, stir yeast into water to soften. Add milk, eggs, pumpkin, butter, 2 cups flour, brown sugar, salt, cinnamon, ginger and cardamom to yeast mixture. Beat vigorously for 2 minutes.
Gradually add remaining flour, a little at a time, until you have a dough stiff enough to knead. 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. In order to cut down on drag, 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, butter, vanilla, and lemon juice to a small food processor. 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. (I used 2 cups powdered sugar).
Frost warm rolls with the cream cheese frosting and serve immediately.
For night before prep: Prepare the rolls up to the point where you roll and place in the pan. Then, cover in plastic wrap and refrigerate overnight. In the morning, remove the pan from the fridge and proceed with the instructions where you left off. Rising time may be slightly longer than noted in the recipe due to the dough being cold vs room temperature.