Make the dressing. In a blender combine all the dressing ingredients except for the sesame seeds. Blend until well combined. Add the sesame seeds, pulse two or three more times. Pour into a small bowl and set aside until ready to use.
Poach the chicken. In a large skillet combine all the ingredients for the chicken. Bring to a simmer over medium heat. Turn the chicken over, cover and gently simmer for about 10-15 minutes or until chicken is cooked through. (Adjusting heat as necessary to keep the chicken at a gentle simmer, a hard boil will produce tough chicken.) Remove chicken from poaching liquid and let rest for 5 minutes. Slice thinly. Toss with a spoonful or two of the dressing.
Finish the salad. Combine all the vegetable components in a large bowl, add the dressing and toss gently to combine. Divide salad onto individual plates, top with chicken and toasted almonds.