Heat a nonstick pan on medium-high heat. Once the pan is very hot, add the oil and crumble in the turkey, saute quickly to brown while breaking it up into smaller pieces until no longer pink, then remove from the pan with a slotted spoon, leaving the grease in the pan. Add the mushrooms and broccoli to the pan and saute until the mushrooms start to brown and soften, then add the garlic and ginger; saute for another 2 to 3 minutes.
Stir the broth, sesame oil, soy sauce, peanut butter and vinegar until well combined. Bring to a simmer and reduce to concentrate the flavor. Adjust the seasoning with salt if needed then remove from the heat.
Bring a large pot of water to a full boil. Cook noodles following the instructions on the package. Once cooked, drain and quickly rinse under cold water for a few seconds to remove any surface starch and stop the cooking process.
Return the pan to medium heat, toss the sauce with the noodles and turkey. Garnish with scallions and red pepper flakes.