Toss the shredded kale with 1 tablespoon of the lemon juice and a pinch of salt. Squeeze everything together with your hands several times to start to gently soften the kale's toughness. Set aside.
Meanwhile, toss the sliced shallot with the remaining lemon juice and set aside. Let both the kale and the shallot marinate for at least 30 minutes. Then, toss them together along with the sliced radishes, cheese, olive oil, and salt and pepper to taste. For each sandwich, spread a toasted roll generously with lemon-basil aioli on one half. Smash half of an avocado on the other half and sprinkle with a pinch of salt. Pile on some kale salad, close the sandwich and eat. Simple!
Lemon-Basil Aioli: Whisk together the lemon juice, zest, egg yolk, and garlic. Whisk in the oil very slowly; start with one drop at a time and work up to a thin, steady stream as the mixture starts to thicken and emulsify. You can also whip everything together in a blender or food processor, but aioli made by hand has a better texture. When enough oil is incorporated to reach your desired thickness, you can stop adding it and fold in the basil and salt and pepper to taste.
Refrigerate for at least an hour before using to allow the flavours to settle and develop. (you can also just stir the lemon juice, zest, garlic, and basil into about 2/3 cup of store bought mayonnaise and it will be really good).