Add 3/4 cup warm water to a small bowl. Sprinkle 1 tsp yeast on top and stir to dissolve. Allow the yeast to activate (about 5 minutes).
In a large mixing bowl (or stand mixer), add the sugar, egg, salt, pumpkin pie spice, pumpkin puree, heavy cream and shortening. Mix to combine.
Pour in the activated yeast and mix.
Add the flour to the mix. Use the dough hook attachment on a stand mixer and mix on medium speed until all of the ingredients are combined and dough is smooth but still slightly sticky.
Form a ball with the dough and place in a greased bowl. Cover and let rise for about 1 hour.
Use a deep sided heavy pot and add 3 inches of vegetable oil. Heat over medium high heat until oil reaches between 360°F – 370°F.
While oil is heating up, combine powdered sugar and pumpkin pie spice and place in sifter.
On a lightly floured surface roll out the dough until it is 1/2 inch thick. Cut into 2 1/2 inch squares.
Working in batches fry the beignets until golden brown, about 1 minute on each side.
Use tongs to remove the beignets from the hot oil. Place on a paper towel lined plate to drain. While the beignets are still warm, dust them completely with powdered sugar/pumpkin pie spice mix. Serve immediately.
Grab all your sauce ingredients and place them by your stove.
Add sugar to a medium pot and start cooking on LOW-MEDIUM heat. Stir constantly until sugar becomes liquid-y and a light amber color.
Cook for an additional 6-9 minutes until it's a true amber color. Add the butter and stir until melted.
Slowly add the heavy cream, stirring the entire time. It will bubble up as you add it all.
Remove from heat and add the cinnamon, vanilla and dash of salt. Stir and whisk until smooth. Sauce will thicken up as it cools.