In a bowl, combine all the ingredients until creamy. Season with salt and pepper. Cover and refrigerate.
In a large bowl, mash the eggs with a fork. Add the mayonnaise and combine while crushing until creamy. Season with salt and pepper. Cover and refrigerate.
In a bowl, combine all the ingredients. Season with pepper. Cover and refrigerate.
Spread half of the chicken salad on the first slice of bread. Cover with a second slice of bread. Spread half of the egg salad and cover with a slice of bread. Continue with half the ham salad. Repeat with the remaining bread and salads to obtain six layers. Finish with a slice of bread. Press lightly.
With a bread knife, gently remove the crusts to neatly square off the sandwich. Cover with a layer of cheese spread. Cover with plastic wrap without touching the cheese (use toothpicks, if needed). Refrigerate for at least 2 hours. Garnish with basil leaves and pink peppercorns or to your taste.
Once the sandwich loaf is sliced, you can freeze it, separating each slice with parchment paper.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.