Cook pasta in a large pot of boiling, salted water until al dente, 8-10 minutes.
Meanwhile, heat oil in a large saucepan over medium heat. Add garlic, jalapeno and ginger; cook until garlic is soft, about a minute. Add coconut milk, cover and turn up heat to bring to a simmer.
Add kale and spinach; cover and cook until just wilted and bright green (depending on the size of your pot, you may need to add it in bunches, letting a handful wilt then tossing in another handful).
Add mint and remove from heat. Puree sauce using an immersion blender (or a regular stand blender - just puree in batches or the steam created can blow the lid off). Add salt in big pinches, tasting as you go, until the flavours pop - then it is properly seasoned.
When the pasta is cooked, scoop out a cup of the pasta water before draining it. Toss the pasta with the sauce, adding splashes of pasta water if needed to thin out to desired consistency.