Preheat the oven to 375 degrees F (190 degrees C). Grease a bowl and 2 loaf pans.
Stir yeast in warm water in a bowl until dissolved. Let sit until yeast starts to foam, about 5 minutes.
Stir pumpkin, milk, shortening, sugar, salt, cinnamon, ginger, and cardamom into the yeast mixture. Add eggs and 3 cups flour. Beat, using an electric mixer on medium speed, scraping down the sides of the bowl as needed, about 2 minutes. Mix in remaining flour, 1/2 cup at a time, until dough pulls away from the sides of the bowl.
Turn it onto a lightly floured surface and knead until smooth and elastic, 8 to 10 minutes.
Place dough in the greased bowl and turn to coat. Cover with a clean cloth and let rise in a warm place until doubled in volume, 1 to 1 1/2 hours.
Punch down dough and turn onto a lightly floured surface. Divide dough in half; form into loaves and place into the prepared pans. Cover loaves with a clean cloth and let rise until doubled in volume, about 30 minutes.
Bake in the preheated oven until top and sides are brown, about 35 minutes.