Prepare the roasted shiitakes: Preheat the oven to 400°F and line a large and small baking sheet with parchment paper. Toss the shiitake mushrooms with the olive oil and tamari and toss to coat. Spread in an even layer on the large baking sheet. Roast for 25 to 30 minutes or until browned around the edges. On the second sheet, roast the carrots for the dipping sauce.
Make the carrot ginger dipping sauce: In a blender, combine the roasted carrots, water, olive oil, rice vinegar, ginger, and salt and blend until creamy. Chill until ready to use and set aside the shiitakes until you're ready to roll.
Make the sushi rice: In a medium saucepan, combine the rice, water, and olive oil and bring to a boil. Cover, reduce the heat, and simmer for 45 minutes. Remove the rice from heat and let sit, covered, for 10 more minutes. Fluff with a fork and fold in the rice vinegar, sugar, and salt. Cover until ready to use.
Assemble the maki sushi rolls. Place a small bowl of water and a kitchen towel near your work area as your hands will get sticky. Place one nori sheet, glossy side down, onto a bamboo mat and press a handful of rice onto the lower two-thirds of the sheet. At the bottom of the rice place your toppings (see picture). Don’t overfill or it will be more difficult to roll. Use the bamboo mat to tuck and roll the nori. Once rolled, use the bamboo mat to gently press and shape the roll. Place the roll to the side, cut side down. Repeat with remaining rolls.
Use a sharp chef’s knife to cut the sushi. Wipe the knife clean with a damp towel between cuts.
Sprinkle with sesame seeds. Serve with the dipping sauce, tamari, and pickled ginger, if desired.