Bring a pot of water to a simmer and gently place the eggs into the pot. Cook the eggs for 7 1/2 minutes. Immediately use a slotted spoon to transfer the eggs to a container of ice water to stop them from cooking any further.
When completely cooled, peel the eggs and coarsely chop them. Place in a large bowl and add the shallot, chervil, chives, mustard, lemon juice and aioli. Toss to combine. Add salt and pepper to taste. Refrigerate until ready to serve.
For the carrot-cider vinaigrette:
In a large bowl, combine the shallots, carrot, vinegar, mustard and thyme. Allow the ingredients to stand for about 10 minutes. Slowly whisk in the oil. Add salt and pepper to taste.
Toss the kale with some of the vinaigrette. Season with salt and pepper if needed.
Toast the bread over a medium-hot grill. Spread a generous layer of the egg salad over the toast, then top it with some of the kale slaw. Cut into four pieces and garnish with the radishes.