Bring a large pot of water to a boil. Cook noodles until tender, about 5 minutes or according to package directions. Drain noodles, return to pot and toss with sesame oil. Cover pot to keep noodles warm.
Meanwhile, heat oil in a large skillet over medium-high heat. Add pork, breaking up with a spoon, and season with salt and pepper. Stir in garlic, chiles, and ginger. Cook, stirring occasionally, until pork starts to brown - about 5 minutes beyond when it is no longer pink inside.
Stir in chicken broth and scrape up any brown bits stuck to bottom of the pan. Stir in peanut butter, soy sauce, rice vinegar and brown sugar. When sauce starts to thicken, add the spinach, a handful at a time, allowing one handful to wilt before adding another.
Divide noodles among four bowls. Top with pork and peanut sauce, then sprinkle with green onions and chopped peanuts. Allow individuals to add crushed chile or chile oil to taste.