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 (120° to 130°F). 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 375°F 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.