Combine 1-3/4 cups flour, sugars, undissolved yeast, orange peel, salt, and pumpkin pie spice in large mixer bowl. Heat milk, water, and butter until very warm (120o to 130oF). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add eggs and 1 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes.
Roll dough on lightly floured surface to 1/2-inch thickness; cut with a 2-1/2-inch doughnut cutter. Knead together trimmings; let rest 5 minutes, reroll and cut. Place doughnuts on greased baking sheets. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Deep fry at 375oF for 2 minutes or until browned, turning once. Drain on paper towels to remove excess oil. Sprinkle with Sugar Topping or drizzle with Powdered Sugar Glaze.
Cinnamon Sugar Topping: Stir sugar and pumpkin pie spice together in small bowl. Sift mixture over warm doughnuts.
Powdered Sugar Glaze: Combine powdered sugar, pumpkin pie spice and milk in a bowl; stir until smooth.