While you are bringing a large pot of water to a boil, hold bunch of kale together, slice off and discard thickest part of stem (about 1 inch). Still holding kale in a bunch, slice remaining stems and leaves as thin as you can.
Set kale in sinkfull (or large bowl) of water and swish vigorously to remove any grit. (Repeat this process with fresh water if kale seems especially sandy.) Lift out kale, place in colander and rinse thoroughly.
When water has come to a rolling boil, add pasta and cook for 5 minutes less than cooking time indicated on package.
Add kale stems and leaves in a few batches, pressing down with back of large spoon to submerge each batch. Continue cooking, uncovered, over high heat until kale and pasta are tender, about 5 minutes. (Kale tends to remain on top of pasta. Press it under water from time to time with back of large spoon.).
Drain pasta and kale and return to pot. Add sesame oil and tamari and toss with fork. Taste and add more sesame oil and tamari if necessary. Add sesame seeds and toss again. Serve hot or at room temperature.