Slice the chicken breast into thin, bite-sized strips and finely mince the garlic and fresh ginger.
In a high-speed blender, combine the firm tofu, white miso paste, honey, and 0.25 cup of the chicken broth; blend until the mixture is completely smooth and creamy.
Heat the toasted sesame oil in a large pot or deep skillet over medium heat, then sauté the minced garlic and ginger for 1 minute until fragrant.
Pour the remaining 0.75 cup of chicken broth and the tamari into the pot and bring the liquid to a gentle simmer.
Add the chicken strips to the simmering broth and cook for 4-5 minutes until the chicken is opaque and cooked through.
Add the baby bok choy and udon noodles to the pot, simmering for another 2 minutes until the noodles are loosened and the greens are vibrant and wilted.
Reduce the heat to low and pour in the blended tofu mixture, stirring constantly for 1 minute until the broth transforms into a thick, luscious sauce that clings to the noodles.
Transfer the udon and chicken to a large bowl and garnish with thinly sliced green onions and sesame seeds.