Fill a 5-quart / 4.7 L pot two-thirds full of water, add the salt, and bring to a boil over high heat. While it heats, dice the peppers, slice the scallions, mince the garlic, grate the ginger, and whisk the soy sauce, gochujang, peanut butter, vinegar, brown sugar, sesame oil and pepper flakes in a small bowl until smooth. Add 1 to 2 tbsp warm water if the peanut butter is stiff.
Add the spaghetti to the boiling water and set a timer for 1 minute less than the package says, usually 8 to 9 minutes. Just before draining, scoop out 1 cup / 240 ml of the cooking water. Drain, return the noodles to the empty pot, and cover to keep warm.
While the noodles cook, heat the oil in a 30 cm / 12-inch high-sided skillet over medium-high for 2 minutes until it shimmers. Add all the turkey, press it into one flat layer, and leave it alone for 3 minutes until the underside is deeply browned. Break it into crumbles only after that, because turkey stirred too early steams, turns grey and dries out. Cook 5 to 6 more minutes until no pink remains and a thermometer reads 165 F / 74 C.
Push the turkey to the sides of the skillet. Add the peppers, scallion whites, garlic and ginger, and stir for 2 minutes until the peppers brighten and soften slightly and the garlic smells fragrant.
Pour the sauce into the skillet with 1/2 cup / 120 ml of the reserved noodle water. Simmer for 1 to 2 minutes, stirring, until it coats the back of a spoon. Add the noodles and toss with tongs for 1 to 2 minutes, adding more noodle water 2 tbsp at a time until the sauce is glossy and clings to every strand.
Take the skillet off the heat and stir in half of the scallion greens. Serve right away in wide bowls with the remaining greens and a lime wedge.