Heat olive oil in a medium pot over medium heat and sauté the diced yellow onion, minced garlic, and grated fresh ginger until fragrant.
Whisk in the pumpkin puree and chicken bone broth until the liquid is smooth and well combined.
Place the chicken breast into the pot, bring to a gentle simmer, and poach for 12-15 minutes until fully cooked, then remove and shred with two forks.
While the chicken cooks, prepare the soba noodles in a separate pot of boiling water according to package instructions, then drain and set aside.
Return the shredded chicken to the pumpkin broth along with the chopped kale, simmering for 2-3 minutes until the kale is tender and bright green.
Place the cooked soba noodles into a large bowl, ladle the hot soup over them, and season with sea salt and black pepper before serving.