Begin by rinsing the sushi rice under cold water until the water runs clear. This removes excess starch and helps the rice cook evenly. Cook the rice in a rice cooker or a pot according to the package instructions. Once cooked, let it cool slightly.
In a small bowl, mix together the vinegar, sugar, and salt until dissolved. Gently fold this mixture into the warm sushi rice. The seasoning will add a delightful tanginess to your kimbap.
While the rice is cooling, slice the cucumber into thin strips, julienne the carrots, and cut the pepper into thin slices. You want all your vegetables to be uniformly cut for even distribution in the rolls.
Place a sheet of nori on your sushi mat, shiny side down. Wet your hands to prevent sticking, then take a handful of seasoned rice and spread it evenly over the nori, leaving about 2 inches at the top edge.
Arrange a few pieces of smoked salmon, cucumber, pepper, carrots, and a dollop of cream cheese across the center of the rice.
Using the sushi mat, carefully lift the edge of the mat closest to you and start rolling away from you, tucking the filling in as you go. Roll tightly but not too tight, as you want to avoid squeezing the fillings out. Moisten the top edge of the nori with a little water to seal the roll.
Using a sharp knife, slice the kimbap into bite-sized pieces. Wipe the knife with a damp cloth between cuts to ensure clean edges. Serve with soy sauce or sesame oil for dipping if desired.