To Poach the Chicken: Put the breasts in a medium saucepan with the soy sauce and just enough water to cover chicken. Bring to a boil, cover, and remove from the heat. Let stand, covered, for 30 minutes. Remove the chicken breasts from the poaching liquid and reserve the liquid for another use. Let the chicken cool, then tear the meat into bite-sized pieces.
To Make the Dressing: Combine the mayonnaise, sugar, vinegar, sesame oil, soy sauce, cayenne, garlic, ginger, and cilantro in a blender or food processor and puree until smooth. Refrigerate until ready to use.
Caramelized Almonds: Melt the butter in a small skillet over medium heat. Add the almonds and saute until golden, about 2 minutes. Add the brown sugar and stir to combine. Spread the almonds on a baking sheet, separating them. Set aside to cool. When completely cooled, the almonds will have a hard, candied coating.
To assemble the salad: In a large salad bowl, toss the chicken with the lettuce, carrots, noodles, and dressing. Top each serving with some of the caramelized almonds and sesame seeds.