Roast the pumpkin in a single layer on a well-greased sheet until brown and tender, about 20 minutes; let cool.
* I puréed the rest of the pumpkin to make Pumpkin Mushroom Pot Stickers or freeze for later use.
Place a nori sheet on a bamboo mat that is well wrapped in plastic wrap. Have a cup of cold water on your workspace. Using wet fingers, spread a thin layer of rice on most of the nori sheet, leave a 1-inch space at the top of the sheet with no rice on it (this will be where you seal the roll). If your fingers become sticky, moisten them again and continue. Sprinkle the sesame seeds lightly over the rice.
At the bottom of the sheet lay 2 logs of pumpkin, side by side across the rice. Do the same with the cucumber logs and scallion strips. Using the mat, roll the sushi away from you from the bottom toward the top into a tight roll. Use a bit of the water to wet the 1-inch strip left with no rice on it to seal the roll tight. Lightly wet your knife to cut the roll into 6 to 8 clean pieces.
Spicy Mayo: Place all ingredients in a bowl and grate the garlic in. Stir well and serve with pumpkin sushi, pickled ginger, soy sauce and wasabi paste.
Serve with spicy mayo, wasabi paste, soy sauce and pickled ginger.