Chop the cauliflower into chunks and place them in your food processor. Pulse until the cauliflower becomes the size of rice. You might need to do it in 2 batches.
Transfer the cauliflower rice to a pan over medium-low heat. Sauté for 10 minutes until it releases most of its water and softens. Mix in the erythritol and rice vinegar.
Transfer to a bowl and add the softened cream cheese and mayonnaise. Mix until combined. Transfer to the freezer for 10 minutes.
Peel the cucumber and cut it and the carrot into long slices. Slice the avocado in half, cut the seedless part in half again, and slice thinly. Cut the salmon into two equal-sized pieces.
When ready to assemble, lay a bamboo mat on a clean surface. Cover with a sheet of nori and add the seasoned cauliflower rice. Spread it using a spoon until even.
Starting at the side nearest you, add the cucumber strips, carrot, avocado, and salmon horizontally across the rice. Roll up the bamboo mat as firmly as you can. Press as you go, using a hand to keep ingredients in place as needed.
When your futomaki has been rolled, use a clean, wet knife to slice it in half. Clean the blade between slices and cut each half into four, giving you 8 equal pieces. Serve with your sides of choice.