Strip the kale leaves off the stem. Discard the stem or slice it very thinly if you’d like to use it.
Slice the kale leaves very thinly and put in a serving bowl. With a little olive oil rubbed onto your palms, massage the kale leaves until they turn bright green and soften. This will take a minute or less.
Cut the romaine leaves lengthwise through the midrib, then slice thinly crosswise.
Add the sliced stem (if using), romaine, apple, carrots, and sesame seeds to the bowl with the kale. Toss together, and season with pepper and a pinch of salt.
Combine the avocado, tahini, lemon juice, water, and cumin in a food processor or blender. Process until completely smooth.
Pour about ½ cup of the dressing over the kale mixture and toss together. Serve at once. Pass the dressing around to embellish individual servings.