Begin by making an avocado sauce. Scoop out the avocado flesh and place in a blender. Add the lemon juice, salt, and cayenne and blend briefly. While the machine is running, slowly drizzle in the olive oil, using just enough to make a thick and creamy sauce.
Next make the sunchoke filling. Combine the shredded sunchokes, pecans, and red pepper in a bowl. Add one or two tablespoons of avocado sauce, a bit at a time, to moisten and help to hold the mixture together. Season with pepper and more salt to taste.
Spread a thin layer of avocado sauce on each slice of bread. Spread a generous scoop of sunchoke filling over four of the slices of bread, then top with basil leaves to cover. Add lettuce, tomato, and top with another slice of bread. Enjoy!