Place the apple cider vinegar, water, sugar, and salt in a small, heatproof bowl. Microwave until the sugar has dissolved-- about 2 minutes. 

Place the carrots in a large jar or other airtight container. Pour over the liquid mixture and transfer the carrots to the fridge to cool for at least ten minutes. 

Combine all of the ingredients in a small bowl. Set aside until ready to use. 

Rinse the rice until the water runs clear-- about 2 minutes. 

If using a rice cooker, add the rice and water and cook according to the manufacturer’s instructions. 

If using the stovetop, add the rice and water and bring to a boil. Reduce the heat to low and cover. Simmer on low for 15 minutes, then turn off the heat and allow the rice to sit for 10 minutes. 

Combine the rice vinegar, sugar, and salt in a small, microwave safe bowl. Microwave until the sugar and salt have fully dissolved-- about 1 minute. 

Pour the mixture over the rice and stir the rice constantly for 5-7 minutes, or until it is cool to the touch. Cover with a damp towel and set aside until ready to use. 

Wrap a sushi rolling mat with plastic wrap (this will help keep it clean). 

Place a sheet of nori on the rolling mat. Press about ? cup of sushi rice onto the mat, making sure to go all the way to the edges on three sides, but leaving about 1” of exposed nori on the side farthest away from you. 

Add a few slices of carrot, cucumber, and avocado to the nori on the side closest to you. 

Starting from the side closest to you, roll the Nori up over the filling and continue rolling (as tightly as you can) until you reach the end of the rice. 

Brush the last 1” of nori with water and then roll it to seal. Use the sushi mat to seal the roll tightly. 

Using a sharp knife, cut the sushi into 6-8 slices, depending on how large you like them. Garnish with sesame seeds and spicy mayo. 

Enjoy immediately.