Whisk together pumpkin, oil, eggs, pumpkin-pie spice, 1 1/4 cups sugar, baking soda, and salt in a large bowl until smooth, then whisk in flour mixture until just combined. Fold in optional walnuts, if using.
Stir together cinnamon and remaining 1 tablespoon sugar in another bowl.
Divide batter among muffin cups (each should be about 3/4 full), then spinkle tops with cinnamon-sugar mixture. Bake until puffed and golden brown and a wodden pick or skewer inserted into center of a muffin comes out clean, 25 to 30 minutes.
Cool in pan on a rack 5 minutes, then transfer muffins from pan to rack and cool to warm or room temperature.