In a medium bowl (or a large bowl if you want to toss the noodles in it later), whisk together the peanut butter, white miso, soy sauce, rice vinegar, honey, and water until smooth and pourable. Set aside.
In a separate bowl, mix together the garlic, gochujang, soy sauce, rice vinegar, and honey for the chicken. Set aside.
Slice the shiitake mushrooms into strips. Cut the cucumber into matchsticks.
Roughly chop the cilantro. Thinly slice the green onions. Set everything aside so assembly is easy later.
Heat a large skillet over medium-high heat and add a small drizzle of olive oil. Add the mushrooms and sauté for 4–5 minutes, until softened and cooked through. Remove from the pan and set aside.
In the same skillet, add the ground chicken. Cook over medium-high heat, breaking it up as it cooks, until fully cooked through and any excess liquid has evaporated.
Add the prepared gochujang sauce and stir well. Let it bubble for 2–3 minutes until glossy and evenly coating the chicken. Remove from heat.
Bring a pot of water to a boil and cook the udon noodles according to package instructions. Drain well, reserving a little cooking water just in case.
Add the hot udon noodles to the bowl with the peanut sauce and toss until fully coated. If needed, add a splash of reserved noodle water to loosen the sauce.
Divide the noodles between bowls. Top with the spicy ground chicken, sautéed mushrooms, cucumber matchsticks, cilantro, and green onions.
Serve warm.
