Slice avocado into thin slices. Peel and de-seed cucumber and slice thinly.
Cover bamboo mat in saran wrap or with a Ziploc bag.
Lay a sheet of nori, shiny side down, on the mat.
With wet fingers (dip in rice vinegar or water), spread 1/2 cup rice onto nori.
Sprinkle with sesame seeds, and then gently flip over (not you, the nori sheet with rice).
Place 1/4 of the veggies in the center of the sheet. Roll sushi, pressing tightly on the mat for a firm roll.
Slice into 6 pieces. If knife gets sticky, dip in rice vinegar or water. Repeat with remaining nori sheets and vegetables.
Serve with soy sauce and/or wasabi, or make your own spicy sauce as explained below. Chopsticks optional.
For the sauce, mix 1/3 cup mayonnaise with 1/4 cup ketchup and 1 teaspoon each of cayenne pepper and garlic powder. Add a drizzle of coconut milk to thin to desired consistency.