To prepare the no-cook rice, peel the jicama and cut it into chunks. Transfer those to the bowl of a food processor. Secure the lid, and pulse briefly until the jicama has a rice-like texture.
Transfer the riced jicama to a thin dish towel, then squeeze as much excess moisture as possible from the veggie rice. You can collect the juice in a bowl or drain it over the sink. Once the excess moisture has been removed, the rice is ready to use without cooking.
To create a spicy 'tuna' replacement, place the sliced roasted red peppers in a small bowl. Add the sriracha and stir well, then set this aside.
Place a sheet of nori on your bamboo rolling mat. The lines in the nori should look vertical to you. Fill the lower 2/3 of the nori with a flat layer of jicama rice.
Add a horizontal, single layer of avocado on top of the rice. Then add a layer of spicy roasted red peppers, and a few thin pieces of carrot and cucumber.
Starting at the bottom of the roll, use your bamboo mat to roll the bottom over the veggies, tucking them in tightly. Roll the nori almost all the way, leaving about an inch at the top. Get your fingers wet and add some water to that final section to help seal the roll.
Transfer the roll to a cutting board and use a very sharp knife to slice the roll into pieces. You will get 6 to 8 pieces per sushi roll. Repeat the process with your remaining nori sheets and sliced veggies.
Serve these rolls right away with a dipping sauce of tamari mixed with freshly minced ginger. Leftover sushi rolls can be stored in an airtight container in the fridge for up to 4 days.