In a small bowl add yeast and warm water; let sit 5 minutes.
In the bowl of a stand mixer fitted with a paddle attachment, add in milk, eggs, pumpkin puree, oil, salt, pumpkin pie spice, maple syrup, sugar, yeast/water mixture and 2 cups of flour. Mix on medium speed for 2 minutes.
Switch to dough hook attachment. On low speed, slowly add in remaining flour, 1/2 cup at a time, until dough is firm enough to knead. Not too sticky. Knead on medium speed for about 6 minutes or until dough is smooth and elastic.
(For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface.)
Turn dough into a oiled bowl. Cover; let rest in a warm spot and allow to rise until doubled in size.
Punch down dough, and turn out onto a floured surface. Roll dough out into a large circle, about ¾-inch thick.
Using a 2 to 3-inch round cookie cutter, cut out doughnuts. Place them on a parchment-lined cookie sheet. With the extra dough scraps you can shape ring-shaped doughnuts or roll them into balls for "doughnut holes." Cover; let rise until double in size.
Meanwhile, preheat cooking oil to 365°F degrees in either an electric fryer, or on a stove top in a heavy-bottomed Dutch oven.
Once the doughnuts have risen, fry 1-3 at a time depending on how large your fryer or pot is. Fry for approximately 2-3 minutes flipping half way through the process to evenly brown. Once they are golden brown remove from oil with a spatula and place on paper towels to "drain". Once all the doughnuts are done, allow to cool.
Prepare filling: With an electric mixer whip cream cheese until light and fluffy. Slowly mix in 1 teaspoon heavy cream, powdered sugar and cinnamon. If it appears too thick, mix in 1 teaspoon of heavy cream at a time until desired consistency is reached.
Prepare icing: Whisk maple syrup and powdered sugar together until smooth.
Assemble doughnuts: Poke a small hole straight through the center of each doughnut, going all the way to the back but careful not to cut through the other end.
Fill piping bag with the cream cheese filling. Using a with a medium sized tip, fill each doughnut with the filling.
Spread maple glaze over the tops of each filled doughnut and sprinkle lightly with sea salt.
If you have left over frosting and icing spread onto fried doughnut scraps as well.