Cook pasta: Boil pasta in salted water according to package directions. Drain (do not rinse). Allow pasta to cool for about 10 minutes.
Make sauce: Combine soy sauce, peanut butter, rice vinegar, ginger, sugar, and garlic in a microwave-safe bowl. Microwave on high for 1 minute, just to soften the peanut butter and heat the mixture. Remove from microwave and whisk until smooth. Stir in sesame oil.
Combine: Combine cooked spaghetti, shredded cabbage, shredded carrots, and sauce until evenly combined. (At this point, the noodles can be refrigerated up to a day before serving.)
Top and serve: Just before serving, stir in green onions. Top noodles with roasted peanuts. Serve noodles warm or chilled / room temperature.