Slice the chicken breast into very small, thin strips and season with sea salt and black pepper.
Heat the sesame oil in a non-stick skillet over medium-high heat. Add the chicken and cook until browned, about 5 minutes.
Add the minced garlic and grated fresh ginger to the skillet, sautéing for 1 minute until fragrant.
Pour the coconut aminos over the chicken and simmer for 2-3 minutes until the liquid reduces into a sticky glaze. Remove from heat and let cool slightly.
Prepare the vegetables by julienning the carrots, cucumber, and red bell pepper into thin matchsticks, and finely shredding the cabbage.
Fill a large shallow bowl with warm water. Dip one rice paper wrapper into the water for 5-10 seconds until it begins to soften, then lay it flat on a clean surface.
Place a portion of the glazed chicken and a handful of the julienne vegetables in the center of the wrapper.
Fold the bottom of the wrapper over the filling, tuck in the sides, and roll up tightly like a burrito.
Repeat the process with the remaining wrappers and filling. Serve immediately while the wrappers are soft and the vegetables are crisp.