Cook the pasta according to the package instructions. Drain your pasta and set aside.
In a large skillet over medium-high heat, add the oil, cabbage, and ½ teaspoon salt. It will seem like a lot of cabbage at first, just let it cook, stirring every 2 minutes or so, until it wilts down and gets nice and browned, about 10-12 minutes total. Remove from heat.
In a medium bowl, whisk together the tahini, lime, sesame, soy, and garlic until combined. The mixture should be thick but pourable. If too thick, stir in a splash of water (this really depends on how thick your tahini is).
Add pasta and sesame sauce to the skillet and toss to combine. If after you toss it, the sauce seems too dry or you want it more saucy, just add in splashes of water until it’s your desired consistency. If it gets too runny, just simmer it until it reduces.
Serve topped with lots of green scallions and sesame seeds.