Cook the spaghetti according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the sesame oil over medium heat. Add the minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add the chopped kale to the skillet and cook for 3-4 minutes, stirring frequently, until the kale is wilted.
Stir in the cooked noodles, soy sauce, rice vinegar, salt, and pepper. Toss everything together until well combined and heated through, about 2-3 minutes.
Remove from heat and sprinkle with sesame seeds and sliced green onions before serving.