Trim the excess fat from the chicken and cut it into thin strands. Season with salt and pepper, and set aside.
In a bowl, whisk together heavy cream, milk, mayo, salt, and pepper.
Finely chop the onion and slice the carrots thinly on a mandolin.
Slice the potatoes into thin pieces, using a mandolin. Rinse the potatoes under cold water and pat dry.
Combine the onions and potatoes in a bowl, and season to taste.
Add the onions and potatoes to the bottom of a 9x13 baking dish and top with fresh herbs.
Add the carrots over the potatoes and then layer the chicken on top.
Evenly spread the sliced butter, then pour the milk mixture over all the ingredients.
Garnish with shredded cheese and cover the dish tightly with foil.
Bake in the oven at 400°F for 60-90 minutes, checking the potatoes for doneness.
Garnish the dish with fresh herbs before serving.