Whisk first 5 ingredients in medium bowl to blend.
Using electric mixer, beat sugar and eggs in large bowl until very thick, about 3 minutes.
Add spices and vanilla. Gradually beat in butter;
Beat in sour cream and pumpkin puree.
Gently fold in dry ingredients in 4 additions (dough will be slightly sticky). Cover; set.
Sprinkle 2 rimmed baking sheets lightly with flour. Press out 1/3 of dough on lightly floured surface to 1/2- to 2/3-inch thickness. Using 2 1/2-inch-diameter round cutter, cut out dough rounds. Arrange on floured sheets. Repeat with remaining dough in 2 more batches. Gather all dough scraps. Press out dough; cut out more dough rounds until all dough is used.
Using 1-inch-diameter round cutter, cut out center of each dough round to make doughnuts and doughnut holes.
Line 2 baking sheets with several layers of paper towels. Pour oil into large deep skillet to depth of 1 1/2 inches. Attach deep-fry thermometer and heat oil to 365°F to 370°F. Fry doughnut holes in 2 batches until golden brown, turning once, about 2 minutes. Using slotted spoon, transfer to paper towels. Fry doughnuts, 3 or 4 at a time, until golden brown, about 1 minute per side. Using slotted spoon, transfer doughnuts to paper towels. Cool doughnuts and doughnut holes completely.
Cinnamon Maple Glaze
Whisk ingredients together until creamy.
Drizzle or doughnuts or dip doughnuts into the glaze
*in the United States Maple syrup is graded either A or B. Grade A syrup is light amber colored and very mild in flavor.
Grade B is dark and richly flavored with almost floral undertones. I prefer Grade B for baking and cooking and use Grade A for cocktails and sauces.