There's no raw fish in these easy sushi rolls—just succulent, perfectly cooked salmon and plenty of fresh vegetables. For our food editor's tips on how to roll like a pro, see How to Make Sushi at Home.
Preheat oven to 400 degrees. Rinse rice in several changes of water, jostling rice with fingertips, until water runs clear. Set in a sieve over a bowl to drain while you prepare the rest of the ingredients (at least 20 minutes).
Using a mandoline or vegetable peeler, slice ginger paper-thin along the grain (to yield 1/2 cup). Bring a small pot of water to a boil, add ginger, and blanch 5 seconds; drain. Return pot to stove and add 3/4 cup vinegar, 2 tablespoons sugar, and 2 tablespoons water. Season lightly with salt. Bring to a simmer, stirring to dissolve sugar. Reserve half the vinegar mixture (this will be used to season your rice); add blanched ginger to remaining vinegar mixture and set aside. Cool completely.
Place rice and 2 1/2 cups water in a small pot. Bring to a boil, then reduce heat to lowest setting and cover. Cook until rice is tender and all the water has been absorbed, about 12 minutes (alternatively, cook rice in a rice cooker according to manufacturer?s instructions). Remove from heat. Let sit with lid on, 10 minutes more. Transfer rice to a large bowl; cool 5 minutes. Fold in one-quarter of the reserved vinegar mixture with a wide spatula or plastic bench scraper, fanning the rice while you fold in vinegar mixture to cool it down quickly. Cover with a clean kitchen towel. Reserve remaining vinegar mixture for assembling.
While rice cooks, season salmon generously with salt and let stand 10 minutes. Pat dry. Meanwhile, toss cucumbers and carrots with remaining 1/4 cup vinegar, 1 teaspoon sugar, 1 teaspoon salt, and sesame oil. Set aside. Roast salmon on a parchment-lined rimmed baking sheet until just cooked through, 8 to 10 minutes. Cool, then flake into 6 portions.
To assemble, place 1 sheet of nori, shiny-side down, on a bamboo rolling mat with the long side closest to you. Dampen hands with reserved vinegar mixture and gently press 3/4 cup rice evenly across nori, leaving a 1/2-inch border on all sides. Spread 2 teaspoons mayonnaise evenly across center of rice. Layer 1/3 cup vegetable mixture, 1 portion salmon, and a few slices of avocado evenly across middle of rice. Sprinkle with sesame seeds. Starting with the edge closest to you, use the mat to fold the bottom third toward the center, pressing evenly across the roll to compress the filling. Repeat with another turn and gently press again. Remove mat. Lightly wet a sharp knife with vinegar mixture and cut into 6 equal pieces. Repeat with remaining sheets of nori. Serve with reserved pickled ginger and soy sauce.
If you don't have a bamboo mat, you can line a clean kitchen towel with plastic wrap and use that as a guide for rolling.