Cook the rice (instructions here). In a large pot, add water, chicken, the white/light green parts of the scallions, ginger, garlic, soy sauce, and salt. Give it a gentle stir to combine, then bring to a boil over high heat, then cover and reduce to low to maintain a gentle simmer for 7 minutes. Use tongs to flip the chicken over, cover again, and simmer for 4-8 more minutes or until the chicken is cooked through (depends on size of breast, 160F).
Transfer the chicken to a cutting board. Continue to simmer the broth rapidly, uncovered, over medium heat for about 5-7 more minutes to reduce it a bit. Remove the ginger, scallion, and garlic chunks (or pour the liquid through a strainer into a liquid measuring cup).
In a high-speed blender (a small or personal sized blender works best), add all of the sauce ingredients. Blend until totally smooth. Slice up the chicken.
To assemble, scoop rice into a bowl. Pour some of the broth into the bowl. Top with sliced chicken, cucumbers, and lots of herbs. Spoon some of the sauce all over the chicken. Top with more sesame seeds and dig in!